:confused;

When I try to copy an asset from one project to another, the asset is replaced
by an already existing asset in the project. For example. Say in Project1 I
have Assets A and B. In Project 2 I have Asset C. When I try to copy asset C to
Project1's stage I see asset A or B. It is never consitant. I need to copy
assets I have done this before without an issue. Any thoughts?

Don't drag assets from stage to stage.

This is very strange. They have different names? And Flash starts to mix them
up? Did you check whether their linkage ID's are different as well?
If all that's the case I would try to scan the disk for errors, then I would
try with fresh empty files, and if that fails, too ... well finally attempt a
clean install of Flash. Something must have been corrupted.
Hope for the best
Wolf