mas svou kocku. is that also correct?
svoji and svou are interchangeable?
Maybe,it is more closer to "You have your own cat"?
I would translate that with "svoji vlastní".
Are there different form of "you" in Czech, as there is in Russian more formal "вы" and informal "ты"?
Yes and it is the topic of the Thou skill which you will encounter very soon. They sound almost the same in Czech: ty and vy.