possible for supermassive black holes up to a certain distance from the singularity. To my knowledge there's still the possibility of ring shaped singularities that could be passed through and we don't really know yet what would happen there. Unified quantum gravity theory needed first, so remains in the artistic freedom of the director.
* how did he pass through the Schwarzschild radius with his simple spaceship
Again the only question is whether the tidal forces would be too strong and a supermassive black hole does not have extremely strong forces at its event horizon.
* why was there no time dilation as he approached the black hole
I think there was. After returning from the closely orbiting planet they had a few decades such that he now was a bit younger than his daughter, after coming out of the black hole another 50-60 years have passed for the outside world. Granted though, as far as I understand GRT, actually entering a black hole takes literally forever from the point of view of the outside world (i.e. time breaks down completely), but again, we don't know what would happen with quantum gravity, so maybe the infinity would cancel out somehow if our theories were better.
* why did his spaceship break down inside the black hole but he was able to eject with his simple spacesuit and survive
Tidal forces act the stronger the more vertical distance from the gravitational center an object has in itself (i.e. the height of the object from the singularity's point of view). A spaceship is much larger than a human, so it will break down earlier.
* how did he realistically survive out in cold space (at the end, yes okay I know this is technically possible but still..)
You do have a few minutes in space - the coldness isn't actually a problem since nothing can transport heat in a vacuum. It's rather the pressure difference that will give you trouble, but there are some measures such as emptying your lungs that will give you more time.
* how did he survive inside a black hole
possible for supermassive black holes up to a certain distance from the singularity. To my knowledge there's still the possibility of ring shaped singularities that could be passed through and we don't really know yet what would happen there. Unified quantum gravity theory needed first, so remains in the artistic freedom of the director.
* how did he pass through the Schwarzschild radius with his simple spaceship
Again the only question is whether the tidal forces would be too strong and a supermassive black hole does not have extremely strong forces at its event horizon.
* why was there no time dilation as he approached the black hole
I think there was. After returning from the closely orbiting planet they had a few decades such that he now was a bit younger than his daughter, after coming out of the black hole another 50-60 years have passed for the outside world. Granted though, as far as I understand GRT, actually entering a black hole takes literally forever from the point of view of the outside world (i.e. time breaks down completely), but again, we don't know what would happen with quantum gravity, so maybe the infinity would cancel out somehow if our theories were better.
* why did his spaceship break down inside the black hole but he was able to eject with his simple spacesuit and survive
Tidal forces act the stronger the more vertical distance from the gravitational center an object has in itself (i.e. the height of the object from the singularity's point of view). A spaceship is much larger than a human, so it will break down earlier.
* how did he realistically survive out in cold space (at the end, yes okay I know this is technically possible but still..)
You do have a few minutes in space - the coldness isn't actually a problem since nothing can transport heat in a vacuum. It's rather the pressure difference that will give you trouble, but there are some measures such as emptying your lungs that will give you more time.