Basically the title.

I don't see any options for it in the Posting settings, so I ask. Can I set a submition as private (so only I can see it)?
If yes, can I change it to public any time later?

no

Short answer: No.

Long answer: e621 is not a personal art gallery, nor does it have any sort of gallery focus; and is simply an image board like the various Booru sites out there. The only furry site I'm aware of that at this time allows private submissions until made visible by the uploader is InkBunny.

but why tho

Chaser said:
but why tho

Guessing its because all their 'art' so far has been bad edits of existing pieces and they got tired of them being deleted?

https://e621.net/post/deleted_index?user_id=280028

E621's purpose is to share art work. If you want to have a system to favorite and tag images that isn't e621, then try one of those things that tags it on your own pc.

ara8a883 said:
Basically the title.

Can I set a submition as private (so only I can see it)?
If yes, can I change it to public any time later?

If you want private submissions, leave it on your hard drive. Anything you upload here is public.

There's Deviantart's sta.sh feature that makes things private before you upload them.
Maybe e621 could have similar, but idk, it seems useless. Just use Deviantart. The staff probably won't stalk your sta.sh.