http://www.white-peacock.com/FGM.jpg

Zone 5a. Are these the annual or perennial kind? I had 2 envelopes of
seed from the same place. One gave me some FGM's that form a small
clump with long, ovoid leaves and bloom in the spring, seem to be
perennial although some seem to have died off because of neglect.

These are different, I scattered them in a porch box and had to put
chicken wire over it because of chipmunks which got most of them. I
planted them this spring, and now they are starting to bloom.

The red arrow shows how the first bud cluster starts to form.

I googled and found cynoglossum and myosotis types.

If these are the perennial form, I need to find a permanent spot for
them in my garden and try to transplant them. When would be the best
time? Full sun? Part shade? They get mostly sun where they are now.
Should I just leave the box outside over the winter and transplant in
the spring or do it now?

If they are annuals, the best I can hope for is that they will self-seed
in the box.