I would very strongly advise against this connection.
Without even considering any possible delays:
Online check-in for Israir from Athens is apparently not possible.
It's unclear what the check-in deadline is. Flights to Israel and/or involving Israeli airlines often have specific security measures, which require additional checks before check-in and/or at the gate, and this often means extended delays. There's a page somewhere on the Israir site (in Hebrew only) which talks about "starting checks no later than 3 hours before departure", but it's quite unclear what they mean.
For reference, El Al in Zurich say "check-in no later than 3 hours prior to departure" and "El Al security Check at the Gate no later than 2 hours prior to departure time". In Geneva it's 2 hours for check-in.
I haven't found anything about that on the Israir website. They probably tell you only once you have actually booked your ticket.
So it's not clear whether it's actually even possible in this case, and if it is, how much margin you have. My guess is that's it's either not possible at all or extremely tight, with no margin for any delays.
As for your second question, even if you buy the two flights at once on MyTrip or other funky OTA, they are still two separate tickets, which means that if you miss a deadline (check-in or boarding) for the second flight, for any reason, you're most likely to find your ticket cancelled and to have to buy (and pay for!) a new one, at last minute prices (usually much more expensive). So if you still want to make that self-transfer, buy the tickets yourself directly with the airlines, you'll save yourself a lot of hassle.
The usual rule of thumb for self-transfers is to have at least 4 hours between the two flights, but in this case I would probably increase that quite a bit more. Also given the times, and the higher probability that the next flight is the next day, that makes it even more risky.
Don't do it unless you don't care having to buy a new ticket at last minute prices and/or having to stay overnight in Athens (on your own dime).
Finally, a search for MyTrip or IsrAir on this site would probably be informative.