As for them bathing, they can't take a bubble bath, they must have a special type of dust.

They roll in a type of volcanic ash to free their fur from oils, whether they come from us/our hands, or everyday humidity. They should be offered this bath at least twice a week, but some keep it available everyday. I do not seeing it can be damaging to the fur, causing split ends & rough fur. (& it would be WAY too messy.)

i use a kind of dust called, Blue Cloud. You can buy it online, & in bulk of 50 pounds, less, or more. It's better than the other kinds in pet stores & most people that show their chinchillas use it. I like it a lot & so do the chillas.

Chinchillas shed in season. But its not too bad, normally it all comes out in their dust bath.

Dust bath should be changed after a few uses. (So no fungus creates in there & then the dust will be light, & night in clumps.)

Chinchillas dont require much attention to their fur other than the dust bath, you can brush them with a fine comb though.  They cannot get lice or fleas, since their fur is so thick!