Uploading paper drafts before first-time publication
In my view, you're overthinking all of this.

Unless you've got strong mentors collaborating, your first papers are likely to be terrible. Your work might be wonderful, but writing scientific papers is a specialized skill, and you haven't really practiced that skill yet if you haven't had a paper go through scientific peer review.  So if you want to publish, you should start submitting and start building those skills.

My strongest advice here would be to try to start working with one of your professors as a mentor (and likely co-author).  They are likely to be much better able to assess what is needed to make a good publication out of your work. If you've actually accomplished something interesting, they are more likely to offer such mentorship.

If you have a very strong ability to withstand rejection, you could also go ahead and just submit your papers to what you believe is an appropriate journal (make sure it's actually reputable, and not a predatory piece of junk!).

Finally, the biggest red flag to me in what you've written is talking about being secretive about your work. Even if you're onto something wonderful, you should be thinking about this as not as your magnum opus but as just the first in a very long series of publications that you will make over the course of your career. Being secretive is often a trap, which causes people to think their work is more important than it is because they aren't getting outside feedback on it. 

Let go of the fear, find a mentor co-author or send in your manuscripts yourself, and learn from the (likely harsh) feedback that comes from the reviewers.