I'm a faculty member in a Canadian university who hires a lot of RAs (and who has sat on hiring committees), so I can speak to this.
In general, you need to really watch the balance you take on. The extra money is great, of course, and if you need the funds you ultimately should take these positions - the hourly rate is good.
In terms of CV building: some RA ...
The value of these types of RA positions lies in the connections and research experience (seeing up close how a successful faculty member puts together high-impact papers, learning skills).
You should select RA positions based on whether the position is likely to position you well for relationships with high-productivity scholars in your area. These can then ...
You should certainly list it, whether it is treated as a big deal or not. It won't have a negative impact. But if it is a formal course with evaluation and a grade, then it probably also shows up on your transcript. In that case, listing it again, probably has less value.
But, in an application for grad study, you could list it as part of your motivation for ...
I would suggest something like "left to pursue PhD" rather than "quit" or "abandoned". The explicit meaning is the same, but there is an implicit negativity in quitting or abandoning something.
PhD student, Dept of Rocket Science, University A, 2016 to present (expected Spring 2032)
MA student, University B, 2015-2016 (left to ...
Your second version seems clearest, but the wording might be "Abandoned on acceptance to doctoral program". And state on the first line that you are in a doctoral program. Give complete years for BSc.
Doctoral Program, University A, 2016 to present
MA Program, University B, 2015–2016 (abandoned on acceptance to doctoral program)
B.Sc., University ...
Yes, you can do that, but it won't mean a tremendous amount in any evaluation. But probably better to list it than not. And the section you suggest is the correct place for it.
It is immaterial whether you have published there or not, assuming, only, that the journal is reputable.
A service section would be appropriate, optionally with sub-sections including editor, editorial board, and PC, for instance. Service goes beyond peer-review, so you could also have sub-sections including examiner, for example.
The name of the supervisor is not usually needed in a CV. What would be useful is to describe in a few words (or with bullets, your preference) what was your activity, what you've learnt, what you achieved.
You can mention the supervisor as a contact person, in case your new employer require this.
Just something simple. I'll assume the professor is at the same university, otherwise just name the university as well.
Project on Optimal Underwater Symphonic Expression under Professor Charlie J. Tuna.
The details of the professor are relatively easy to find for a reader if they are thought necessary.
Your CV is not the right place to mention this. Instead, you should write a brief explanation near the beginning of your personal statement or cover letter which explains your reasons for applying to a new PhD. I would advise that you think carefully about how you explain your motivations. If you sound like an uncommitted student (even if that is down to ...
As with many things related to hiring, it is not what you know but who you know. The form-letter approach is very obvious (as other answers have mentioned) and professors who aren't actively looking are not likely to give your mail a serious look. Therefore, you should focus on working your advisor's network and your personal network. Then, even if there is ...