To answer parts of the literal question:
You can’t edit a post after the first few minutes if you aren’t registered. You also can’t comment on it without the “comment everywhere” privilege or delete it. That simple.
Edit to clarify:
The original question about the jar of pasta sauce was posted by an unregistered account, note the turquoise gravatar.
The posts after that we’re posted by a registered account with the same chosen user name, which has a pink gravatar.
That means that you can see all posts, including deleted posts younger than 60 days, that were posted by the registered account when logging in as such. You can also edit them or comment on them.
You can’t see deleted posts by your unregistered account. For the system, they are from two distinct users. Which means you can perform only those actions that you could do with any other post and that depends on what your privileges permit.
But looking at the other things that came up, maybe this needs a longer answer, covering more than just the question per se.
First, your actual question is quite interesting and it would be a pity to lose it. As it has an answer and that answer has an upvote, you can’t delete it. See here for details.
Second, all SE sites have a very clear format, which is basically “one question on top and multiple answers below”. This automatically means that all posts in the answer section that are not actual answers to the question will be removed. The community members with enough reputation (“points”) can and will do that via votes and/or flags, or a moderator can do that, if they happen to see it. And this deletion is not negotiable, sorry.
Third, comments are per definition temporary. They are intended for clarification or suggesting improvements. They can be removed any time and without prior warning. The remaining comments under your deleted non-answer starting with “Thank you” weren’t removed manually as they were deleted together with the post.
Four, there is the question about rudeness. Some comments were clearly outside what is considered a respectful discussion, calling users “gestapo” or “liar” when they simply point out something that doesn’t fit the site’s rules is not ok and never will be. These comments were correctly flagged as rude by a user and handled by a moderator accordingly.
It is within your rights to delete some1 of your posts. If you happen to be using the app (instead of the website), the “delete” can be tricky to find, it’s the little ‘x’. Maybe this screenshot will help?
It’s a known issue, but I don’t know when or if it will be fixed.
1 Again: Within the limits outlined here.