Is it possible to submit a paper to a scholarly, peer-reviewed journal without PhD and get it accepted?

Submitting an academic paper for publication (and potentially getting it accepted) does not require any qualifications whatsoever. You don't need a PhD; you don't even need to have gone to college. There are no educational, employment, or membership requirements at all.

That's not to say it's easy to get a paper accepted with no formal training in the field. Learning how to write a compelling paper is much easier if you have a mentor to offer guidance. However, if you can figure out how to do it without a PhD, then your lack of a PhD will not be held against you.

Yes, it's possible to get a paper published without having a PhD: PhD students do it all the time. Submitted papers are supposed to be evaluated according to what they say, not who said it.

Yes. In practice, graduate study is one of the main ways people attain the skills to write such a paper, but a Ph.D. is not a requirement. Qualifications would be a choice of the individual journal, but I don't know of any that have a policy of requiring degree credentials from submitters. For example, quite often graduate or undergraduate students write such papers.