Yes you can definitely bathe a pet rat. In fact it is important for its health. Here is a link to a website that offers step by step instructions to bathe your pet rat.

http://www.wikihow.com/Bathe-Your-Pet-Rat

 It's not only good for their health, it's good for the smell they carry. It's not that bad of an odor, but it can be if you don't bathe them once a month. Some rats even like water. Mine did. He'd swim like all get out!!!

 Yes , one of my real good friends bathes her rat bailey.. It gives him a refreshing look smell everything

 Yes here are reasons why:
Cleans them
get rid of oder
good for health
fun
Try not to squeeze them to much though.