How do I know that 'go' is referring both to who i am visiting as well as who's house it is?
the issue is more complicated. "go" is mostly referring to "him" - who I am visiting, but we don't use possessive pronouns in Polish as often as they are used in English. In Polish it is vague if it is a new house/the new house or his new house, but "his new house" is assumed.
I think you can, but you are putting much more stress on the word "him" than when using "go"
it is not. Instrumental would be domem. It is locative. It is after w, indicates location , and does not mean to/into.,
nowym is singular masculine instrumental=singular masculine locative=plural dative.
there were hints missing, which unfortunately happens a lot.