1)Yes, it is decidable for string W. As, for a given string, if it is finite, it is enough to tell it is decidable. But if we think it's prefix, yes number of prefix in a finite string is countable. So, 'yes' answer possible here, but we cannot say 'no' for any given string. Hence it is partially decidable or semidecidable.
2) It is undecidable. What the string actually telling? it is asking if input= output? So, we cannot decide if both input and output strings are equal or not.Equality doesnot imply decidable property.Hence, undecidable
3)For every input prefix there is one output. Which means output doesnot depend on input. Say for output phi, there are inputs phi, 0,1,11,001.............. Here nonmonotonic property of Rice Theorem satisfies. Hence it is not even partially decidable.