Ok, this is very well written article explaning some problematic parts that people don't understand. But there is one more paradoxal point I didn't get it why and how the writers could not figure it out that, if a nation can't survive in itself and needs help from aliens (later cooper finds out that these aliens are actually us, who are already in 5 dimensional universe) to solve the equation for their existence and if people would die without help of outside, how could their descendens survive and then live in 5 dimensional world to save their ancestors?! This is pure paradox and not possible. And it's very well known that one can be in the future but can't go or change things in the past, even in 5 dimensional universe.
Murph figured the physics out by herself. Her father knew plan A was a pipe dream, and he did abandon her.
She couldn't bear hating her father. The movie is her elaborate fantasy about her father telling her the answer. So elaborate, she hallucinated him on her deathbed. Her father never came back through the wormhole.
That is known as the bootstrap paradox (http://en.wikipedia.org/wiki/Bootstrap_paradox). You could argue that the entire point of the movie is to highlight this specific paradox that can result from time travel. As with most time travel paradoxes, and pretty much anything related to time travel, it's not known exactly how things would work out in the real world.
Perhaps in some parallel universe the humans survived and figured out a way to travel between the different universes, and decide to cross over to help this universe survive.
