"They eat pizza in the kitchen." suggests that it's something they do in general. "They are eating pizza in the kitchen." defines an action they are doing right now. I'm pretty sure you would have to use a different form of їдять in order to communicate a general action done at a non-specific time.
There is no present continuous tense in Ukrainian, so both sentences are translated in the same way. You need more context to tell if a repeated action is meant or if the action is taking place right now.
You can tell a repeated action from a continuous one for verbs of motion, because they usually have the respective pairs of words. For example, "іти" - "ходити" (to go). "Вони йдуть до школи" -- "They are going to school (right now)". "Вони ходять у школу" -- "They go to school."
I did not notice the article. You used the present simple tense instead of the present continuous and that is what I considered OK.
I think it is better to omit the indefinite article here, because you are talking not about some pizza here, but about a kind of food. So "pizza" is a mass noun here and should be used without an article.
There is a number of false friends in Ukrainian and Polish: porttfel (wallet in PL) -- портфель (briefcase in UK), dywan (carpet in PL) -- диван (sofa in UK), ...