Why every finite set is computable?
A similar question was answered here:

How can it be decidable whether $\pi$ has some sequence of digits?

We can ignore the question "if a given TM halts" as it is irrelevant what the question actually is, let's just name the condition C.

If C is true, then the correct algorithm is if n == 0 return true else return false. If C is false, the correct algorithm is return false. Whether C is true or false, one of these two algorithms is correct for every n, so such an algorithm exists.

Additionally, "does a given TM halt" is computable for the same reason - the correct algorithm is either return true or return false. What is not computable is a function that answers "does this TM halt" for any TM.