proč nejde kateřině jsou čtyři měsíce
Cause we're not talking about Kateřina's age.
Exactly, it's not her age, it means that she is in fourth month of pregnancy.
"Kateřina je ve SVÉM čtvrtém měsíci" is accepted but "svém" is really not needed here?
Not only it's not needed, it's also much more natural without it. It's only accepted in case some people would object that the sentence can be translated literally. But to speak about pregnancy, it's surely much better without it.