There's also the fact that she would have gone through the gate with 3 or more cats, so she might end up in the End of Time and who knows what after that
That is an interesting possibility if gina and gasper hooked up. I wouldn't necessarily say crono's father, (although anything dealing with crono's dad would probably be one of the biggest holes that could be filled in expanding the story) as that would leave to all sorts of time complications.
Well how many cats she went through with shouldn't really matter. Weren't all the gates already connected to the End of Time? How else could Ayla, Magus, Frog, and Robo all enter the same gate and get to their home periods?
I think this is where we draw the distinctions between story mechanics, and gameplay convenience. My understanding is that each gate leads to a specific endpoint. You are brought to the end of time the first time because of the laws of time travel gate mechanics, blah blah. After that, they would be traveling through specific gate points to get to specific destinations, not necessary take the EoT everytime. I assume, then that from that vantage point, the other party members are able to glimpse part of the time streams (so they know whats going on, and not need to be updated every night by the campfire) or at least hear it from Gaspar, who does seem to see aspects of the flow of time.
what's Gaspar do at the end of the game?
He's either stuck at the EoT, or chooses to stay there. On the stuck idea, I was reading in various articles about how the BoT and EoT take on various qualities based on each person, ie, it looks or can look different to each person. I just finished a play through of the game, and Gaspar mentions you can only travel through gates you've been through, meaning each person. Gasper ended up there from a time anomaly created by Lavos, so either the only gate he see's is the one to the destruction of Zeal, or there isn't a pillar for him at all since it wasn't an "entity" gate that brought him there in the first place.
So, why doesn't he then leave with crono and gang on the epoch? That could be a possibility, or because of the changes he's undergone during his stay there (when he's confronted as being the 'guru of time' he acts like thats not him anymore) so he stays there either as convenience, or he feels he has more to do there.