it's not finitely generated because which is a subgroup of is not finitely generated. (recall that every subgroup of a finitely generated abelian group is finitely generated)
it's not free because it's not torsion-free. for example has finite order.
2) Is free Abelian group?
it is finitely generated because it's generated by and
no it's not! a non-trivial finite group is never free!
3) Is free group?