Are the sentences correct?
Playing ball games can cultivate friendship because most ball games are playing by groups. Participants can meet more new friends.
Is it correct to say it like this?
Most ball games are usually group games so participants can meet new friends.
Okay, except that you wouldn't use both "most" and "usually."
Most ball games and group games...
Ball games are usually group games.
I don't want to be bitchy, but I think the reader doesn't need to be reminded that ball games are almost always group games. That's pretty obvious. If it were a ball game played by one, he wouldn't be meeting new friends there.
I'd still prefer the version I suggested above, but yours is good English.
I love jai alai. I hope you'll get a chance to see it while you're in Spain.