What case is 'to' in here? Accusative?
Yes, „to museum” is a noun phrase acting as a direct object in this sentence, so it needs accusative.
My friend is very often visiting this museum
The above not accepted can you tell me my error please
Well, as far as I know, you don't really use Present Continuous with adverbs of frequency like "often"...
Is "to" an absolute requirement here?
Well, it says "this museum", like in the English sentence.
I totally missed the "this", I was thinking the "to" was some sort of "do" substitute...