If it doesn't have cheese, is it still a pizza?

Yes! In fact in Italy you will find several pizzas that do not contain any cheese. Some infact have on top, salad leaves, cream fraiche, eggs and so forth.

Yes of course. The definition of pizza is a type of bread crust with toppings, and the toppings are up to you. Even though cheese is a popular topping for pizza, not every pizza has to feature it.

There are also white pizza recipes without tomatoes, even though tomatoes feature on 99% of pizza recipes. A white pizza is topped with garlic, herbs and cheese, so it is white or cream-colored. I love making my own pizza recipes and white pizza is one of my favorite kinds (I also like the hearty meat feast ones of course!)

sure, If it is pizza by the way pizza don't have to have tomato cheese.

Not in my opinion. Otherwise, I'd just call it a flatbread with toppings.

why not?

Pizza is pizza

Yes it is, but unusual.

No.