@sdtkd03 - First, about connecting with a professor, obviously the first place to start is making connections with various math teachers in your high school, any lecturers/sponsors of local math circles, math competition coaches, etc. There is no substitute for just asking around, and expressing an interest. I will be frank, depending on where you are it probably will not be easy because mathematics does not generally require “lab assistants” or similar, but give it a try! My own kid forged some relationships with local professors by helping to administer and work with the local middle school math circle which was sponsored by a local university.
Are you doing anything this summer? It is probably too late to apply for Canada/USA but I think HCSSiM and maybe MathiLy should still be possible. Both will take 9th graders. If you are already near JMO level, and you enjoy math for its own sake (not just to rack up some competition points) you should have a decent shot at either or both. Let’s hope they are not cancelled because of corona fears…
SUMaC does engage in a group research project. My understanding is that it is more like guided reading based on a number of open questions that faculty/lecturers attending have, and that the project culminates in a group presentation, but rarely in a publishable paper. SUMaC is relatively short at 4 weeks, so that also limits the ability to delve too deeply. My knowledge, though, is only based on a few kids I know who were accepted but chose to attend other programs, so take it for what that is worth. SUMaC is very expensive compared with other camps if that is a concern.
Ross and PROMYS are very similar in structure and content. However, my sense from someone who attended Ross three summers ago after sophomore year (and recently placed in top 250 in the Putnam as a freshman college student) is that Ross is more freeform, with much more solitary work. It is very cerebral and tranquil, less structured than PROMYS. I know someone who went to PROMYS last summer after junior year and she confirmed this view. Boston of course can be more fun than Columbus, and I do not know what Ross is like now that it has switched campuses from OSU, but it has been going on for more than 40 years I think, so they probably do not change too much. I am sure that you know that both Ross and PROMYS are almost exclusively number theory. I believe that Ross would be better for independent work that might some day lead to a publishable paper.
Canada/USA will also have research projects that you can join (or form), based somewhat on the SUMaC model (it is dependent on the interests and specializations of the lecturers/faculty). Canada/USA though by its nature is very broad, so there will be many potentially interesting topics to choose from.
MathiLy has recently added a research option called MathiLy-Est (I think) aimed at college students, so I feel like it is ramping up its research focus. However, the girl I know who attended PROMYS also attended MathIly in an earlier summer, and she felt that mathematically it is not at the same level as Ross or PROMYS or Mathcamp but that it was a lot of fun. My sense is that MathiLy could nevertheless be a very good choice if you are interested in combinatorics.
Last, I forgot to mention one of the main math research programs, again for juniors, MIT’s PRIMES-USA (or PRIMES if you are Boston local). If you do not know that program, you should start looking into it now. There are plenty of entrance exams and solutions floating around on the web. They will give you a good idea of what is expected at a very top research program for high school students. Best of luck, I hope the above is helpful!