The question and answer directly above your question indicate that a "to be friends with" verb-plus-instrumental case construction can be used. But... the instrumental case hasn't been introduced at this point in the course.

So the main translation at the top of the discussion uses a simpler "to be" verb-plus-genitive construction instead. In this construction, the Czech sentence is literally "I am a friend OF those women," and that's where the genitive comes into play.

I hope this makes sense!

Yes, "I am a friend of those women" would make for an easier and more direct translation. Perhaps a change will be considered for the next version of the course.

It does look weird, but the phrase is very often used, at least in the US.

Se has to be the second word, so it's either: Já se přátelím s těmi ženami. or Přátelím se s těmi ženami.