Edit: just realized you were talking about Perchance. The following is about images uploaded to Lemmy. Sorry.

1. As far as I know, the answer is "no", although you can contact the lemmy.world admins/host and ask them to do it, maybe. That doesn't stop it from being hosted off of instances that synced with yours.
2. I assume that Lemmy instances will delete images on really old posts eventually, but I don't know for sure. If there is a retention policy, it probably varies by instance.
3. Probably, but it will likely be buried thousands or millions of images down.
4. Not really.
5. Unless it has credit card info or something in it, I wouldn't worry about it too much. Do what you can and move on. The odds that anyone close to you will find it is low unless they're closely monitoring your account.

Try to do reverse search of image?

To see if it can be found.

Use different sources and search engines, not sure if doing this would prop it up a little though.

Does not get autodeleted after a while that I know of.

If you can't find it in trending nor best and it is beyond where any noncrazy person would find it in recent, I think you don't have to worry (unless the person happens across this post and then scrolls way far back on recent images of the specific generator you are talking about). You can't delete it, but if you find it you may be able to downvote it enough times using one or more accounts that the gallery autohides it. Most galleries have a setting for 'how many downvotes hides an image' in their perchancescript. Often it is like 2