Here are some general comments about your situation. I will NOT comment on the COVID situation and leave that for other answerers, as I don't feel I know enough to be able to comment accurately there.
As a general terminology thing, there are three separate stages: "security" which is checking the contents of your bags for weapons etc., "passport control" or "immigration" which is checking you into (or out of) a country with your passport, and "customs" which is checking what you're bringing into the country (usually you can just walk straight through the "nothing to declare" entrance as a tourist but once in a blue moon you'll be stopped and have your bags checked).
Printing everything shouldn't be necessary but also shouldn't hurt. I'd do it just in case.
Most important thing is to arrive in plenty of time at the airport. Since you're a new traveller it's probably best to aim to arrive the full 3 hours before at Heathrow (though myself I'd probably only leave 1.5-2 hours for a long-haul flight these days); certainly best to have bags of time to hang around in the shops/restaurants than to be rushing at the last minute. Also make sure you go to the right terminal; Heathrow's terminals are more awkward than those at most airports to transfer between, and so you don't want to have to do that. Your Heathrow terminal should be advertised in your booking confirmation. If you're driving/being driven just follow the road signs for the correct terminal number; if you're on public transport, there are separate tube, railway, and bus stations for Terminals 2-3, Terminal 4, and Terminal 5, so go to the correct one.
Usually these days you can check in online or through a mobile app, but with non-budget airlines you can usually check in at a desk or at machines alternatively, if you would rather have a physical paper boarding pass. You may be required to check in in person due to COVID restrictions; I'm not sure. Either way your boarding pass (digital or physical) will tell you what time your gate is expected to close. It might have a gate number listed on it but this could change so don't take it as gospel; check departure boards at the airport. Try not to lose your boarding pass, but if you do, it's not a massive deal as they should be able to re-print one for you at the gate upon boarding. Definitely don't lose your passport though! This is also the time you would drop off any checked luggage, if you had any, at the staffed check-in or dedicated bag drop counters. They may ask you questions like if you packed the bag yourself or if anyone asked you to take anything with you; they're really trying to ask if someone has perhaps tried to get you to smuggle something in for them (perhaps unknowingly). Sometimes there will be a step on a checkin machine instead which will then print out a baggage tag you can attach and then take the whole thing to the bag drop station; just follow the instructions. You will also often get a small self-adhesive counterfoil which is usually stuck to the back of your passport; you'll want to have this in the unlikely event that your bags get lost in the system.
After checkin is security. For security, Heathrow tends to be pretty efficient though it does have its bad days. Have your bag prepared so you can easily remove your laptop, tablet, and liquids from your hand luggage; liquids should be transferred into the provided plastic bags (or if you already have one, you should put them in there at home and just pull that out to save time). You'll also need to remove coins/keys from your pockets, watches, phones, etc. to go into the tray. Everything, including bags, ultimately goes into trays at Heathrow; other airports differ in this aspect where you put your bags directly onto the belt. Remember that you cannot take liquids in containers over 100ml in your hand luggage. Since you're not taking hold luggage this means you can't take anything above this. There are no passport or customs controls when leaving the UK.
Once you're through security, especially if you decide to spend your time in a pub/restaurant, keep an eye on the time and keep glancing at the destination boards every now and again; I've known people to miss flights because they got too relaxed at the airport and lost track of time! Keep the "gate closes" time that will be listed on your boarding pass in mind; you don't want to be away from the gate when that time comes unless you're informed of a delay on the departure boards. There will be plenty of time once the board changes to "go to gate" so don't get yourself into a panic, but certainly you should be on your way to the gate by the time it says "boarding" else you might run into difficulty. Most large airports these days no longer have announcements that flights are about to close etc., because there are just so many flights this is no longer really possible without annoying everyone. Some flights from Terminals 2 and 5 leave from satellite terminals ("B gates" or "C gates", gates will be prefixed by one of these letters). There are trains to reach these which leave very regularly, or you can walk if you have loads of time, but do bear in mind it takes a few more minutes to get down to these terminals. But there aren't usually too many amenities in these so you might wish to stay in the main terminal until it's closer to your boarding time.
I'm assuming you're in economy class since you haven't specified otherwise. For those who can easily sleep in seats, the seats should be reasonably comfortable though you might need to bring a pillow or whatever. You can recline the seat but try to be mindful of the person behind you, especially if they have their tray down/are eating. It depends on the airline but you can usually expect a hot (microwaved) main meal plus an additional small meal (usually just cold snacks) in economy. Personally my strategy for dealing with jetlag is not to sleep on a westbound flight and just count it as an extremely long day. If you can force yourself to stay awake, by the time you get to bedtime you should be so tired that you'll sleep until the morning. But YMMV, jetlag tips vary wildly depending on who you're talking to, so if you do want to sleep on the flight it shouldn't be the end of the world.
Just a little note about when you're on the plane. Above your head will be seatbelt signs, when these are lit you're supposed to return to your seat and fasten your seatbelt securely. In my experience, most European airlines will only use these if there is a genuine safety reason (particularly strong turbulence, takeoff, and landing), so they should be obeyed strictly. But if you're on an American airline, they tend to use them pretty often for long periods of time, basically whenever they'd rather you not be wandering around the cabin. So when flying with an American airline they usually tolerate people ignoring them to get up to use the toilet, for example.
Upon arrival at JFK, be prepared because the airport is pretty grim by European standards, though ultimately it's not that bad. It's just not a particularly pleasant environment even for an airport. You'll firstly go through immigration, I believe this entails answering some questions on a touchscreen terminal, which then prints a ticket for you to go through the staffed booths with. This system may or may not be back in use; reportedly it was out of use during the height of COVID. You might be feeling stressed after the flight, just take your time and read the questions carefully, and you should be fine. Once you speak to a human they'll possibly ask you a couple of questions about the nature/duration/etc. of your trip, just take your time and answer these honestly and you'll almost certainly be fine. Honestly I've never felt threatened or intimidated at US immigration. This is the point where any COVID restrictions will come into play as well, which I am not qualified to comment on.
Since you're connecting onto a domestic flight if you had hold luggage you'd need to collect it to take it through customs (customs doesn't exist for domestic flights which is why it needs to be done then). But since you don't, you can just head straight through customs out into arrivals. The next step at JFK is to find the terminal for your departing flight, and head on the AirTrain free shuttle if you need to change terminals. You'll then need to find your way back into departures, pick up a physical boarding pass if you need/want one, and go back through security. This is just how US airports are I'm afraid, very few of them supply a shortcut for connecting passengers. Security in the US will likely be slightly stricter than at Heathrow; you'll likely be asked to take your shoes off as well. But other than that it'll be similar. Probably worse-organised and a larger queue than at Heathrow, though perhaps not.
You should have plenty of time left for your connecting flight. If a delay or cancellation on your incoming flight leads you to have insufficient time to make your connection, though, you can talk with your airline at their checkin desk for them to book you onto the next available flight at no charge. This is because you have booked it all on one ticket, the connection is essentially "guaranteed" by the airline.
At Pittsburgh you'll just go straight out of the airport, no immigration, no customs, nothing, since it's a domestic flight. So don't expect that to take too long. I've never been to Pittsburgh but there's a very short, frequent train ride you'll need to take from the airside terminal to the landside terminal.
Generally at airports, signage is pretty good so I don't think you'll need to ask for directions. But if you do I'm sure you can find someone to ask.
On your return trip, at Pittsburgh, you'll have to go through security but not any immigration or customs, again because it's a domestic flight.
At JFK you'll have to do all the same stuff in reverse (though note that if you have hold luggage, this may be able to be checked through to your destination since there will be no need for a customs check, so you might not have to collect it; ask the staff on checkin at Pittsburgh); leave into the arrivals area, check your departure terminal, catch the AirTrain if you need to, pick up a boarding pass if you need to, go through security, and finally hang around until your flight. The US also does not have exit customs/immigration checks.
Assuming it's an overnight "redeye" flight, my personal jetlag recommendation (again YMMV) is to get what little sleep on the plane you are able to, which will probably be not very much, then once you arrive, whatever you do do not sleep until the evening. Force yourself to do something if you have to, personally I often work a full day in the office to stop myself being tempted to sleep. By the evening you'll be so tired you'll hopefully fall asleep at the correct time. Eastbound jetlag is MUCH worse for most people, as you'll find yourself lying awake at night until a ridiculous time in the morning wondering why you can't sleep, and it's very unpleasant.
Upon arrival at Heathrow you'll have passport control; you will be directed through automatic passport gates which are reasonably easy to use. You likely won't talk to a human at Heathrow assuming you have a UK passport; though thinking about it this might have changed because of COVID. From there you'll pass through baggage reclaim and straight through the "nothing to declare" aisle at customs - almost certainly (unless you've bought a bunch of stuff beyond the personal allowance). And that's it, you're out!
On the subject of travelling with a checked bag, well, it's up to you. I wouldn't say it adds a huge amount of difficulty, but it likely adds a lot of irritating waiting around. This is why personally I like to travel without one wherever possible. But others clearly have very different opinions to me! Just think of it more as a decision whether you want to add a bit of extra faff at each airport but then not have to carry a bag around versus carrying a bag around everywhere but having less time waiting around by the baggage reclaim belt/in bag drop queues/etc.. I'm sure you can make that decision for yourself which you'd prefer. My point is I doubt it'll make or break your trip which one you choose, and it shouldn't cause you any problems.
