No, not a problem. Everyone interacts a little differently with the story.
The idea with the first part is that it's an unfolding situation. You assume at first that you're AFTER the events of the first game, but discover eventually that you're (briefly) BEFORE those events. It's a fun little reversal of expectations.
Haven in general is meant to be a place you explore. You're given a general idea of what you have to do to progress, but it's supposed to be a place where you can take a moment to just poke around and take in the setting a bit. CS1 immediately tossed you into things, largely out of necessity, but with a bit more to work with in GT I wanted to give a little more context to things. The space isn't meant to be hyper-efficient, at least your first time through. You just explore, bumble around, and eventually figure out where you're going.
As for events in Haven, there is one, and more are planned for future chapters, based on how you play each preceding one. For now though, it's mostly about establishing the setting and characters.
The ending is in keeping with the previous game. I'll probably always end on an epilogue "outro" like that. Obviously there will be fallout from the recovery of the disc, but that belongs in the start of Chapter 3.