Consider what it would look like if you ran the solar system in reverse - all the planets and moons would go backwards in their orbits, but gravity still works exactly the same. The equations of mechanics don't care about time.
And yes, information being lost in black holes would be an issue, if true - that's why that problem has been studied so much recently.
You'd see radiation hitting the planet warming the mantel, complex chemicals breaking down & releasing heat, all warming the planet significantly to the point where it was a molten ball, and finally lots of instability where large explosions were throwing pieces of it into space.
That is what is so unsettling about T-symmetry. What you describe is merely improbable, not impossible. With appropriate starting conditions, it is certain. Basically we'd require all the particles in the comet to bounce into each other in such a way that their heat motion cancels and organizes into momentum in one direction, away from the planet. This is physically permitted in either time-direction, but we only see it in one.
Yes, but the reason you do is that it's merely (and extremely) unlikely, not impossible. The third law of thermodynamics has its own arrow of time (the one in which entropy increases), but the basic interactions of the universe don't need to change to make that happen. They work symmetrically (mostly, with some tiny exceptions as detailed in the linked article).
Gravity gets double-negated when you reverse time. Its units are over seconds squared instead of just seconds.
A simple way to see this is to imagine taking a movie of a heavy back arcing upward through the air then back down. What do you see when you run the movie backwards? A ball arcing upward them downward. The acceleration still points in the same direction: down.
Lets consider only the moment before the collision of the small planet pieces: these are all accelerating to the center of mass.
If you revert time, you still have a lot of pieces, with high speed, but these are going away from the center (and getting slowed by the gravity).
After collision, it gets more tricky, because the kinetic energy of a body will be lost (mostly transformed in thermal energy) and it will be less intuitive to imagine how to revert that.
Interstellar gas/dust forming a planet increases its temperature, and it radiates thermal photons out into space. For the planets to fly apart, you would have reverse the photons as well, and aim them super precisely, and define the initial state of the planet super precisely, and...
It's essentially a problem of entropy. All weirdness of macroscopic time-reversal can be reduced to the weirdly low entropy of the big bang.
So if I understand correctly, time reversal means that all the object speeds get inverted, but the fields remain the same. If you change the sign of the field (gravity becomes repulsive) then things will explode very quickly :)
If you go to the 'overview' section, there is a nice snippet explaining all this. It points out that gravity works fine in a universe that is running backwards, however entropy is decreasing instead of increasing.
Also information might be lost in black holes. Wouldn't that also prohibit it reversing time?