[phoenixheart]

I know someone already answered, but the more the better, right?

Essentially:

1. Word order doesn't matter here. Just a preference thing, in my experience.

2. Depends on which one you want to emphasize, where your cat is or fact that there's a tree with a cat in it.

3. 何 can be used by itself. The ways I've heard it--in anime and in real life--are:

何が? [what is it? (subject)]

何ですか？ [what is it? (nominative)]

何（なに）？[what?]

It can only be in a question sentence, because simply the fact that the word "what" appears in the sentence makes the sentence a question. This is true in all languages.

4. Referring to your eye would be あります。
私は目が二つあります。 (I have two eyes).

Hope this helps!