Social media is standing up on a podium in a crowded street, shouting through a bullhorn. Now you're asking about comming back the next day to tell everyone what you said yesterday is a secret. Do you see how that seems strange?

Privacy lost, can NEVER be regained. When you make something public, that's it. It's public now.

Never post anything to any social media that you might want to keep private. It doesn't matter who owns it, or how it's licensed, if it's online unencrypted, it's public; Now and evermore.

Can I ask the moderators of this instance to delete my posts without a trace so that they are not in the federation database?

A instance admin can only delete your posts from that specific instances database, so you should assume that there will always be some sort of copy of your post (with things like search engine caching and the Internet archive this basically the case on any social media).

Is there a way to chat safely on Lemmy? Alas, I like to communicate with different people from different countries, because I can't help myself, by the way, how then can I pass the keys to my matrix room to others or how can others give their keys?

Not a active matrix user, but the default Lemmy chat is definetly not secure. Lemmy allows you to add your matrix handle in your profile settings so it will appear when someone looks at your profile

You can get your local instance admins to delete the messages from its DB, but you can't do anything for the other thousand or so federated instances, they all have a copy of the messages.

Safely depends on the content of your messages. But generally, consider your messages public.

"A super AI that is perfect at finding people" - firstly, doesn't exist, secondly, by definition cannot be defeated. Otherwise, use e2ee when possible, and talk in person.

No and no.

As far as chat goes, maybe SimpleX or Session. Those are 2 e2ee decentralized chat apps. But you'd have to chat your name somewhere unsecured unless in person