True.
Yes.
The GCF is, yes.
Yes.
The GCF of any two odd numbers is always odd. The GCF of any two even numbers is always even. The GCF of an odd and an even number is always odd.
It is false.
Yes and yes.
The GCF of any set of odd numbers is odd because odd numbers don't have any even factors.
Yes.
Yes.
No, always odd.
Yes.