든 하다

anything at all; any time

-든 on a question word makes an "any" word, and every line here does exactly that: 뭐든 하다 "do anything at all", 무엇이든 (the more formal version of 뭐든), 언제든 하셔도 돼요 "do it whenever you like". It is the shortened form of -든지 and means precisely the same; the short one is commoner in speech. The tone across these lines is permissive — someone telling you there is no restriction.

Register: everyday, permissive