Do any characters fart 或者 burp? Please answer.

Very, er, odd question. XD I'm actually kind of afraid to answer this, but I guess I will anyway since I've got nothing better to do.

Yes, they do. In "The 獭, 水獭 Woman", Rico, Private, Kowalski, and Julien have a burping contest, plus the one from the Kids Choice Awards two years 以前 that Rico entered. And Kowalski let one rip once underwater. XD

I'm pretty sure there are a few other examples too, but I can't think of any off-hand.

Infact they do!
As Penguinangel said, there was a couple burps in "The 獭, 水獭 Woman" by:
- Kowalski
- Rico
- Private
- Julien

And in "Herring Impaired", Kowalski farts underwater while he's lifting the 箱, 板条箱 of fish. XD