well, they do but very little. they would mostly say "baka" which means idiot. other than that if you don't speak formally to people who you are not close enough it's rude.
other cuss words (haha): "kuso" which means "****"
"yarou" means "rascal" and is also not very endearing ^_____^ you could aso say "kuso yarou" if you're really angry! >
ayu does not swear, no. she's too lady to do that. XD