it's not free because it's not torsion-free. for example has finite order. (recall that every free abelian group is torsion-free)

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?