Dan,

1 ,2 and 4 look good.

3.

, here

and

. So the only elements of order 4 are

and

;

have order 2 and

formally has the same elements as

, but

and

. I leave it to you to compute exactly 4 elements of order 4.

So you have the right idea, but your counts are off.

5.

has 13 elements of order 2, whereas

has 9 elements of order 2. This is a lot of computation, but it does show they are not isomorphic. Maybe easier: convince your self that the order of a product of disjoint cycles in a permutation group has order the least common multiple of the cycle lengths. So the maximum order of an element of

is 4 (a 4 cycle), whereas

has an element of order 12.

By the way, I think the usual symbol for a dihedral group is

, the dihedral group with 2n elements (at least it used to be). Also the quaternion group (your notation

) is usually denoted just Q. The generalized quaternion group has 2n elements; I don't remember any standard notation for this generalized quaternion group.

Generally, a good job.