Let me chime in, strictly regarding question 3:
I'd go ahead and try to get academic recs, either from your undergrad professors (it never hurts to ask -- honestly!), or from these Masters classes you mentioned. I applied and got into a fairly well-respected PhD program for stats (although it sounds lower-tier than your desires), and it was crucial that I had letters from faculty. I had been out of undergrad for five years teaching at a top-tier private secondary school, and I thought that maybe I could swing recs from just my superiors there, given my good undergraduate record and excellent GRE scores, but my grad program made it clear that I needed academic recs. I took a year of Masters-level classes, did very well in those, had three of my profs from that school write recs, and got into all of the schools to which I applied.
What's your timeline for applying? Is it feasible for you to take a year and rock out a few classes, like I did, to secure a couple of rec letters? That way, you could get back into student-mode and show your potential schools you're serious about your plans.
Just my two cents...