Does "bratranců" mean all male cousins or could this be a mix of male and female cousins?
If you meant both male and female cousins, you'd have to say "Kateřina má mnoho bratranců a sestřenic."
To answer your question, bratranec (or in plural bratranci) only means male cousin (cousins).
Mnoho, trochu, hodně, málo, pět, deset ... all of these are followed by genitive (a lot OF...).
Dekuji. I see. These are the ¨adverbs of quantity¨ plus some cardinal numbers referenced under the Lightbulb. As I made my way through the lessons, I had forgotten about those, and was focusing solely on the verbs. I think your reminder will clear up some other confusion I had. I am very glad you are here and willing to help.