Will a master student publishing several short papers come across in a bad way? I am a master student in a relatively small research field in humanities. I am a relatively good student: at the moment I’m preparing my bachelor’s thesis for publication in an A journal, and an abstract I submitted for a conference next year got accepted.

Many of my courses are tested with a paper (of varying lengths, anything between four and twenty pages is common). I spend more time on those papers than my peers and in them interact with very recent research papers. I am then tempted to think I could submit a revised version of such a paper (shortening it to 4–8 pages or so, perhaps with a title like “Some notes on...”) to a journal in which the papers I interact with were published. I do not have the illusion a journal would give me the full twenty pages, nor that all of my course papers are valuable enough to be submitted, even in shortened form.

I would like to get published because the review cycle is rather long and starting to submit now could give me some publications to show when applying for a PhD position later. Also, I truly believe that my results are worthwhile.
On the other hand, I’m afraid it may come across as arrogant. All these course projects are relatively narrow-scoped, so perhaps it would be better to keep the results in mind and work them out later, in the master’s thesis for instance, and submit them to a journal then.

Yes, I can ask the teachers in these courses what they think, but don’t want to come across as overly self-confident. I understand you cannot judge my work without seeing it – but perhaps you can give some advice based on the general impression you would get from a master student publishing several relatively short papers.
Try it. It can't hurt.

Having published before starting a PhD program will be seen as an advantage by the people who evaluate your application. It certainly won't count against you, unless you publish in junk outlets and neglect your exams over it, which should be your priority.

This last sentence is important though. It's much more likely to produce publishable results in a BA project than in a term paper. So make sure not to make the perfect the enemy of the good. In the humanities, having one high-ranking publication before grad school is already very good.

In any case, aiming high but realistic will be seen as determined and ambitious, not as arrogant by admissions or your teachers, whom you should also approach for advice and feedback. How you will be perceived of course also depends on how you present yourself.