Could a MOD answer:
1) after being gifted a membership, is it possible to know who gave it?
2) is it possible to delete an old personal topic and if yes, how?
If you send a gift when logged in I'm pretty sure the gift message includes the username of the gifter.
You can only delete content in forums you created that does not have any replies. If you just replied to other posts, you can remove your comments by using a browser and clicking the delete option in the post. If anyone quoted you, those quotes are not impacted.

Could a MOD answer:
1) after being gifted a membership, is it possible to know who gave it?
2) is it possible to delete an old personal topic and if yes, how?