2 Endings, 1 for being fast enough, 1 extended ending for not being fast enough (NTR time!)
There's no actual timer, you have a certain amount of "actions" per phase before NTR happens.
It's not yet implemented, it'll be coming in Chapter 2. The list of current content is on the main page. 6 Main Quests (1 incomplete. Chapter 2 continuation), meaning MQ 6 is the one that's meant to be for Chapter 2.
I hope what you've played so far has been enjoyable and you look forwards to more! If you haven't already, there's a bunch of Side Quest content for you to discover.