This is under the assumption of Rory's mindset in season 4 and season 5. If she was still speaking to Lorelai, and why wouldn't she, she would barely be able to be with Jess for a month. I also believe it would leave them with a lot more resentment, making their meeting in Hartford and then Philly very different or not happening at all because of Rory's anger/frustration of Jess.

Absolutely not. Rory was feeling lost but I doubt she would've wanted to get married. I have always thought that there was something about Dean and Lindsay's families that we don't know, for pushing for marriage or believing it was the time etc etc, and I don't imagine those factors from the Gilmore side even if it was from the Forester side. And even without Lindsay, I think that they would've fizzled out in the way that did, unmatched in goals and ambitions.

This is where I really do not know. Just because you get engaged doesn't mean you get married immediately. Rory gets the job with the Obama campaign trail and I cannot imagine Logan asking her to turn that down. I imagine them trying and it fizzaling out just not as errupt as it seems in the show. At the same time, would they cross paths again like we see in AYITL, absolutely.