Can I submit an abstract to present already published work? I recently finished a project that has accepted for publication in a preventive medicine journal.
I was hoping to submit the abstract to some conferences to improve my presentation skills, and my supervisor informed me that I should make sure my paper is not published before the abstract is presented.
The journal has given us a 12-week ETA on publication, and both conferences I was hoping to present at are much later than that (16-24 weeks). As a result, I was wondering what my possible options are? So far, I have four questions:

If my paper is accepted for an oral presentation instead of a poster presentation, could I still present them if the paper has been published?

Could I ask the journal to put a hold on production so I can present at these conferences?

Does it matter if one of the planned conferences is not international / if they do not publish abstracts?

Should I contact the managing editor to ask if I may present the abstract at the planned conferences?
I think generally speaking you're thinking about your advisor's point the wrong way round. The point isn't that the journal now owns your work and presentations thereof (re: point 2), it owns the copyright, and the right to distribute their presentation of your work.
Rather the point is that conferences are expected to be new work, ahead of the literature. People don't go to conferences to hear a paper read aloud, they go to hear about new things they can't read in the literature. It's a venue for feedback (which can't be applied to a published article).
I'm not in preventative medicine (but at one time was in a medicine-adjacent field), but have heard this before. Generally, an oral presentation might be the better avenue for work that was just published, but you should ask your advisor about point 1.
To point 3 - no.
To point 4 - no, the managing editor is not the one imposing the &quot;restriction,&quot; if you wanted to ask someone besides your advisor, you would ask a conference organizer or someone else familiar with the conference to learn what level of novelty is expected there.