I find that I'm learning by the process of elimination and therefore wondering if I'm really learning.

Yes.
I think you are really learning.
It reminds me of Sherlock Holmes :

How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?

:-)

There are two levels of developing vocabulary: recognition and recall. You have to go through recognition first (what you do when you see the answer in a list) in order to eventually reach recall (when you can think of it without seeing the list). It's just a step in the process.

It means you went home so you don't need to add rumah. But you can say "ke" (to) somewhere to be clearer like "dia pulang ke Jakarta" She went home to Jakarta

Kembali (VERB) = to return Pulang (VERB) = to return home So no, this means going home only. For I am home, you would probably say Saya (ber)ada di rumah(ku)