A 585 is below median at most M7/M12 programs, and honestly strong work experience helps but it doesn't fully compensate for that gap at the very top schools. That said, it's not a dead end either.
On your first question: depends a lot on which school. For Tier 1 (HBS, Wharton, Booth, etc.) the median GMAT Focus is around 720+ and a 585 is a significant gap that work experience alone usually won't bridge. For Tier 2 and regional schools, you have more room. Strong work experience genuinely counts there. If you share which schools you're targeting, people here can give you a more concrete read.
On the second question: yes, retaking makes sense if you're aiming higher. One thing I noticed from your post though: you said you got 16 questions correct in both Quant (Q79) and Verbal (V82) but scored lower than expected. That's because GMAT Focus Edition is adaptive and difficulty matters a lot, not just the raw number correct. Getting 16 easier questions right will score lower than getting 16 harder ones right. So the raw count doesn't map cleanly to the score.
For a 1-2 month retake: I'd start by pulling your detailed score report and looking at where time is being lost. From my own prep, the biggest gains came from cutting down on questions where I was spending 3+ minutes and still getting them wrong. You're not going to gain 100+ points from content review alone in that timeframe. Timed practice and review of your error patterns is what actually moves the needle fast.
Good luck with the retake if you go that route.