Questions about applying to Political Science PhD programs

I’m applying to ~10 competitive political science PhD programs and I have some questions about my applications and my chances. I graduated from UCLA in 2020 and I’m planning to focus on comparative politics, although I might apply as political theory to some programs depending on the subfield of the professors I cite in my SOP. I have 4 questions:

  1. I’ve reached out to a few professors already, a common response I’ve received is that professors don’t tend to talk with prospective students before admissions decisions are made. I have other friends in political science programs who tell me they never received a response like this when applying. Is it worthwhile for me to keep reaching out? I’m mostly just trying to ascertain whether our research interests seem compatible and if they’re taking on students for the following academic year. I’ve also thought about reaching out to current PhD students to ask them about the faculty, is that worthwhile?
  2. Over half the schools I’m applying to have the GRE marked as optional or not required. Does optional really mean optional? I have a very mediocre GRE score (159V, 156Q) which could be considered weak for the schools I’m applying to. I’m thinking of not submitting if I have the choice not to, but is this advisable?
  3. I guess this is more of a “what are my chances?” question, but I’m just trying to make sure I don’t get rejected everywhere I apply to. I’m applying to competitive programs (eg: Stanford, Berkeley, Princeton, UCLA, Yale, UChicago, Northwestern, Georgetown and a few others). I can’t quite determine what a ‘safety’ program would even be in this context since they’re all dependent on what specific professors are looking for. I guess I’ll list my stats for reference:
    a. I graduated with a 3.9 GPA (double majored in Political Science & Geography)
    b. 2 publications as the sole author (although they’re published in undergraduate journals) and 1 manuscript that’s under review (also sole author). ~7 months research experience + a year of teaching experience, I don’t think the teaching matters much.
    c. Good LORs I think, two from UCLA professors and my third letter is from my former research supervisor who’s doing her postdoc at Princeton, one of the schools I’m applying to. All 3 of my LOR writers have supervised research projects I’ve completed and submitted to journals.
    d. My SOP is a work in progress, my former research advisor is helping me revise it. I’m a bit worried that the way I frame my research is confusing and making it harder to create links with professors in these programs. I also state in my SOP that I want to pursue a ‘mixed-method approach’ for my research, combining qualitative and quantitative methods. I’ve taken a college stats class and I’m familiar with R, should I mention these things in my SOP since my GRE quant score is low? One of my published papers also has some quantitative elements to it which I discuss in the SOP.
  4. What else should I be doing? One of the biggest fears is getting rejected everywhere I apply to when I could’ve done something to improve my chances. It’s kind of hard navigating this process mostly alone.