jest*

Cats are dignified creatures after all.

(I wrote it about statements, but the same applies to questions, only the intonation is different and in writing there is a question mark at the end ;-))

When speaking about first (I, we) or second (you) person, one uses verb to be (być) with instrumental to connect subject and predicate. So (ja) jestem psem (I am a dog), (ty) jesteś człowiekiem (thou art a man), (my) jesteśmy fantastami (we are sci-fi fans), (wy) jesteście graczami (you are gamers).

When speaking about third person (somebody or something else), then it is popular to connect subject and predicate by neuter pronoun to: ona to pies or ona jest psem (she is a dog), krzesła to meble or krzesła są meblami (chairs are furnitures) etc.

Clauses like ty to kot are perfectly understandable, but they sound very unnatural.

Emphasis for sure; the second form emphasize te subject more. But as a native, I've never encouterd the second form used in a question, so I'm not entirely sure it's correct.

„Tak”, not „Da”. «Да» is a word in Russian. In Polish „da” has completely different meaning.

We usually don't accept the 'second gender' words for animals, but somehow I do add "kotka" everywhere... so yeah, I can add it here as well.

"Czy" is either at the beginning of the question: Czy jesteś kotem? (it then shows that this is a yes/no question), or it is "or" between some options in the questions: Jesteś kotem czy psem? (Are you a cat or a dog?)

"a", because you show contrast by this sentence :)