1) You're not old. Get over that notion.
2) With a 4.0 math GPA and the courses you've taken, nobody gives a crap about a B- in some bullsh*t introductory course. The F might look remotely bad, but it should seem legitimate that you simply forgot to drop the course, given the rest of your record. Give a one-sentence explanation in your
SOP.
3) The marginal benefit may decrease, but that doesn't mean it's negative. It just means ad coms give a lot of emphasis on analysis, and somewhat less emphasis on additional math. But I can't imagine that any ad com will view "too much math" as a negative. Also, if you're still taking math, it means your skills aren't getting rusty, which is one of the concerns for people who have been away from academics for a while.
4) What's the issue with the significant other? Is it that your S.O. is in a degree program that will take two more years to complete, or just a hesitation on your part to leave (without the S.O., who isn't following for some reason)? The former is a valid concern, and it may make sense to wait another year. The latter is a concern that will be there as long as you remain in the relationship, and you may have to decide between the relationship and the PhD if there's no chance for a compromise. And that is in no way a veiled way of telling you to break up; it's just a way of saying that if you don't address the issue and make decisions now, you may be in the same situation next year and asking the same question.
4) The low-tier school will hurt a bit, but you can still get into a very respectable school. Princeton and Stanford are probably out, but there are people on this board who came from average state schools that ended up in good schools (Minnesota and Johns Hopkins, to name two).