"Any problem whose domain is finite is always Decidable", is true or false?
It's not so clear what is "a problem whose domain is finite". Let me assume that what is meant by this is a finite language. Every finite language is decidable. The Turing machine compares the input to each word in the language, accepts if it finds a match, and rejects otherwise.

This answers your first question. Your second question is a special case of the first one.