Always focus on events during them since you'll get a lot of rewards that you cant get from normal explore or are extremely rare. Each boss you kill gives pretty good rewards such as Wilds or peronamin/pudding. They also give a lot of pero which u can use to buy gatcha tickets.

Personally I'd say you should just progress normally in explore in the days without any event since you'll 1 R girl each stage clear and also have a chance at new n/r/sr along the way from chances. Some people do wait to proceed until they've gotten all of the cards from a specific stage but you don't have to since they will show up again in GHQ, bonus explore stage, or EG explore stage.

You'll be able to catch up eventually since they are so slow in releasing new stages for explore and normally we have 3-4 day breaks between events and also all of Colosseum to spend on regular explore.

For optimal sed growth get your moe cards to like lvl 50 ish since they will give about 80% of their max sed by then. Next you can do either Babe or sexy however sexy give most of their sed in their later levels, opposite of how moes work. Babes have a linear growth.

Extra questions:
1: not sure
2: Get lucky from revival gatcha, you can get 3 tickets for 3m ep in event.
3: revival again
4: NGatcha tickets. If you want you can save for gambit since you get pink keys when you buy Ngatcha to but it wont be for another 3-4 weeks.