Last Spider-Man story, huh? Or to be more precise, the last story with Peter Parker as Spider-Man? Given Slott's "Monkey's Paw" comment and how Peter being a husband and father means he has greater responsibilities and thus more to lose, I'm thinking it's the latter, and that he'll ultimately give up being Spider-Man to be a husband and father. And if "elements from this story will go on into the next incarnation," then don't be surprised if this is paving the way for Peter to pass on the mantle to Miles Morales, making him the "All-New, All-Different Amazing Spider-Man" post-Secret Wars.
Also, since "Last Days" is capitalized, this means that Spider-Man: Renew Your Vows falls under the Secret Wars: Last Days banner, which are supposed to be stories taking place prior to the Marvel Universe being destroyed and becoming Battleworld. In this case, it appears this will chronicle several years of an alternate timeline where Peter and MJ were still married and had a daughter prior to their world being part of an Incursion. Why several years? Because if you remember the original teaser for this, it showed Peter and MJ slightly older with a daughter who looked like she was eight years old (which, interestingly enough, it will have been eight years since One More Day), while the preview images for this are showing Peter and MJ still looking as if though they're still in their late twenties and their daughter is an infant.
As for who the possible Regent is...my guess is if it's not Kingpin, then it's either Mister Negative or The Hood.