Is a(b) a function

Answer 1

No. It may be part of notation that indicates a function, but by itself it does not mean anything and is surely not a function.

Answer 2

It may be a function "a" that depends on "b", though other letters are commonly used for such things (letters "f" and later). It may also mean that you simply multiply "a" times "b".

Answer 3

It can be, but there is not enough information in the question to be sure of that.