My benchmark for whether to continue a game is usually T20. I rarely restart on the first turn for any reason because some of the best indicators of a good start, as whacker mentioned, are neighbors and map layout (for England in particular, those nearby fault lines are really helpful).
On that note, I would say the number one thing holding players back from getting faster victories is conquering. Early conquering/expanding really sets the stage for the rest of your success. I think a lot of players know this but haven't really internalized it. You can wait a surprisingly long time to build districts/buildings in many of your cities; acquiring Rationalism and key gold-boosting policy cards, recruiting Newton, finishing Great Zimbabwe, and larger numbers of envoys all happen around the same time toward the end of the mid-game (around T100 to T125), and the amount of science/gold from infrastructure prior to these game-changers is negligible compared to what you get afterward. Because of this, your early game (pretty much all the way up to T70-T80 or so) should be super-focused on hitting military techs and getting as many cities as you possibly can so that you can aim to complete your infrastructure (with the help of some chopping) in most of your cities right around the critical point at T100ish.
I don't have all your DLC, Sumorex, so I don't actually know how you're doing on number of cities. But your questions, although they are good questions and I agree with whacker's answers, are all about benchmarks for development, which suggests that your priorities may need rebalancing toward more expansion. In particular, Hypatia and Isidore are nice to get, but might not be worth rushing buildings in the early game if it comes at the expense of your army, especially given what you discovered about Hypatia's effect not working for cities conquered after activation (can't believe I never noticed that!).