is it okay to freeze calamari after cooking, even though it was frozen at time of purchase?
All sorts of foods that were once frozen, are thawed, cooked, and then re-frozen for storage.  There is not a safety issue here, as long as the food was thawed, cooked, cooled, and re-frozen properly.  The long-term concern is quality.  There are two issues.  First, dehydration (commonly known as freezer burn) can occur with longer term freezer storage.  Secondly, freezing and thawing often degrades the cell structure of a product, impacting it's texture.  This is often undesirable. You can see other questions on this site about packaging for, and length of time for storage in, the freezer.