How could the daughter of the most powerful force-user possibly have Force powers?

It's truly baffling.

Well, we'd already found out who's Luke's dad, so the film ended with a cliff hanger which would get people talking: why was she able to hear Luke?

I'm more mad at the execution than the fact they did it. No build up to it, and you can practically see the wire.

The issue I had with that particular scene is not that she had force powers. She comes from a force-sensitive family, so her having latent force powers makes sense. Key word here being "latent".

What absolutely did NOT make any fucking sense is A: Leia not dying of asphyxiation when she enters the vacuum of space and B: Leia just happening to know how to use force pull without any prior training. Like, they don't even try to hand-wave it off by saying something like "Oh, she spent some time training with Luke when you weren't looking" or something.