Precisely how such a world would form is, to say the least, tricky to work out. Two planets colliding without first being captured into each other's orbit certainly wouldn't do it--at least, not in one step. Such is a collision is anything but "passive"! As Tim B suggested, it's much more likely to result in vaporizing a large portion of both planets, and creating a ring system and/or moon. If the resulting moon is sufficient large, however, such that you essentially end up with two new planets orbiting each other, that might be a good place to start. Or some other method of capturing two planets into each others' orbit. At that point, you just need some mechanism to rob angular momentum from the system, slowly drawing them closer together, until they distort under their mutual gravity and begin to merge. They have to be pretty close in size for this to work, as otherwise one body will simply break apart into a ring system when it crosses its Roche limit with respect to the other one, and draining enough angular momentum through natural processes is left as an exercise for the reader.
All in all, though, I would gloss over how the planet came to be in the first place, leaving that as a mystery (perhaps even one that you hang a lamp shade on, just so readers know you know that it's a thing, and are purposefully leaving it out rather than being oblivious), and focus on the features of the world as it is, assuming that it does exist. After all, that approach worked fine for Robert Forward in Rocheworld (aka The Flight of the Dragonfly) and sequels.
The "neck" of a peanut world does not have to exceptionally strong. In fact, it can be made of anything at all--even water, or just air (in which case, the system is conventionally known as a rocheworld, like the eponymous novel). This is because a peanut shape is in fact a gravitational equipotential surface; i.e., every point on the idealized surface is at the same gravitational potential, and doesn't want to "fall" anywhere, so no structural strength is needed to support it. That also means that water will not preferentially flow to any particular major region, and you can realistically put oceans anywhere you want. As far as the water is concerned, there is no reason to flow to the outer poles over the neck, or vice-versa. They both have the same gravitational potential.
Now you might think "that makes no sense! Surely the two lobes are gravitationally attracted to each other!" And indeed they are. The catch is that such an equipotential surface only exists if the body is rotating sufficiently rapidly, such that centrifugal force balances that mutual attraction. In effect, the two halves must orbit around each other, close enough that they are touching. And we do in fact know of astrophysical objects that act like that--they are called over-contact binary stars, and they are indeed stars shaped like peanuts (the processes that form over-contact binary stars unfortunately are not easily applicable to solid planets).
In fact, above a certain minimum spin rate, the oblate spheroid shapes that we typically associate with planets become unstable--so if you can figure out a way to start with a normal planet, and then spin it up to ridiculously high speeds, that would give you a way to form a peanut-planet.
So, the peanut planet will of necessity have very short days. Like, on the order of minutes rather than hours. As such, you are unlikely to get lifeforms adapting to the diurnal cycle like they do here on Earth.
The neck region, and generally all non-convex or inward-facing parts of the peanut (i.e., every part of the surface that is not contiguous with the entire surface's convex hull), will also tend to be colder than the outward-facing poles--and this is in addition to the usual decrease in temperatures towards the poles--because they are shaded by the mass of the lobes.
You can also expect some pretty weird wind patterns, due to the combination of high spin rate, non-trivial shape for air to flow around, and non-trivial heat distribution around that shape, but I have nowhere near the expertise to describe them precisely. At the very coarsest level, however, assuming the planet is roughly as "thick" as Earth, through the short axis of one of the lobes, I would expect more and thinner (i.e., covering fewer latitudes) major circulation cells, with stronger prevailing winds. Coriolis effect would also be intense, so you can expect lots of cyclonic storms, but not huge monolithic hurricanes (because if they got too large, they would have to cross cell boundaries).
Now, the surface is an equipotential, but that does not mean that there is equal gravitational force everywhere. Force is the gradient of potential, and while the value of the potential may be the same at every point on the surface, it's gradient is not. You would have the highest gravity at the north and south poles of each lobe, and lower gravity along the equator. Additionally, gravity will decrease from the exterior poles along the equator to the center point of the neck. The lowest gravity would be at the center of the neck on the equator, with the poles of the neck having slightly higher gravity. Depending on just how stretched out vs. squashed together this particular peanut is, the total differences could be very large (like, 2gees at the lobar poles, and a tenth of a gee on the neck), or relatively small (like, say, 1/5th of a gee difference between the highest and lowest gravity areas). The more stretched out the planet is, and thus the higher the variance, the more you would expect both animals and plants to be specially adapted to specific gravitational conditions. Note that the lowest gravity areas, however, are relatively small; the gravity drops pretty rapidly as you move from the convex inner surface of one lobe to the concave surfaces leading into the neck. While the two lobes could have significantly different average gravity between them, the total variance in gravity on one lobe, outside of the concave neck regions, will be fairly small.
Addendum: it may seem that the high rotation rate of such a planet may preclude holding a particularly thick atmosphere, since at some altitude any co-rotating air would be in orbit, and above that altitude it would be actively flung away. The trick is to ensure that the planet as a whole has a sufficiently high escape velocity, and sufficiently distant lobar Lagrange points, that you can keep a suitably deep atmosphere below the escape level, and ensure that a high fraction of air molecules that may escape one lobe nevertheless remain in orbit, to be recaptured later (this is similar to the gas torus phenomenon seen around gas giant moons, notably Io). In the case of a rocheworld, where the bridge is entirely made of air, the Lagrange points are necessarily inside the atmosphere; I am not certain how to explain in detail how such a world is capable of retaining air over the long-term, but Robert Forward thought it was possible, and I'm generally willing to defer to him on such matters. Additionally, the fact that the previously-mentioned over-contact binary stars are not universally surrounded by spiral nebulae is real-world empirical evidence that peanut-world can retain gas, even when the lobar Langrange points are inside the gas envelope; you just need a large escape velocity, which does not necessarily imply a large surface gravity, especially when you have the total mass of two lobes contributing to their mutual escape velocity, but not to each others' surface gravity.
