Commonly speaking you need either tomato sauce or mozzarella to call it a pizza. Without either one, it would be called “pizza pane” but that’s basically flatbread and to be eaten as bread. Pretty rare to find a “pizza” without some sort of sauce to make it wet.
Depends on ingredients but some do not go well with tomato sauce. For example pineapple[0] + blue cheese would be better on white base or no sauce at all than on tomato one.
Italian ortography is not as bad as the english one, but nonetheless is sometimes illogical.
We have a useless lettere 'q' which is pronounced like the the hard c.
'Q' is used only before 'u'.
So there some words that are written with "qu" and other with "cu" only for etymologyical reasons.
The number 4 is spelled 'quattro'.
The pizza with the four cheeses is 'quattro formaggi'.
To be picky, the general rule is that q goes before u only if u is followed by another vowel (qui, quo, qua), c is used in the other cases, but - of course - there are a few exceptions, the most common being "cui".
I think it is mostly about language. Pizza is loan word from Italian in German language in this case. So you may also say it other way around: Pizza counts as flammkuchen.
Yes, besides the toppings, for which there is no rule (there is pizza bianca without tomato, and there is pizza marina without cheese), I believe everybody agrees that pizza dough needs to be made with yeast or sourdough. Flammkuchen dough has neither.