Rohan and Gondor

[Eruwen]

I'm a little confused on these two cities and their inhabitants. When I was reading the LOTR books, I came to this conclusion...

Rohan
Theoden was the king. He had 2 sons and a daughter. One of the sons, I don't know the name of, but the other children were Eomer and Eowyn. In the last battle, Pippin ends up in Rohan.

Gondor
Denethor II is King. He has two sons, Boromir and Faramir. He tries killing Faramir and himself, but fails to kill Faramir. For some reason, Pippin ends up here as well. But I though Merry was in Gondor.

That was my conclusion and thus I am completely lost. Did Merry go to Rohan or Pippin? And is Eowyn supposed to be Eomer's sister? I thought they were both the children of Theoden, but in the movie they have Eowyn as Theoden's neice. They would make that much of a change would they? Can someone please elaborate on this topic for me? I am completely lost.