Considering this show will hopefully have several seasons, much of that narrative has not only not been written, but not even conceived yet so it's a bit early to say what does and doesn't fit in, innit?
No, because this analysis is based on what we've seen, the stated premise of the series, and the nature of the characters as depicted.
One doesn't have to "wait and see" in order to figure out what makes sense narratively for the series and what doesn't.
I haven't commented on the Pilot itself yet, so here we go (bullet-point-style):
* This is perhaps the most 'formulaic' Arrowverse series since The Flash and the one that feels the most like the series that started it all, Arrow, itself
* Luke was based way too obviously and closely on Curtis Holt for me, but I'm hoping that they'll give him his own character sooner rather than later
* It becomes crystal-clear pretty early on that Alice being Beth was never some big 'secret' that the series intended to hide from the viewers, and I'm honestly not sure why the expectation was that it would be
* I think the expectation is that there will be some kind of eventual love triangle/split between Kate, Sophie, and Tyler, but given how firmly the show has based itself on the Arrow template, I don't think this is as crystal-clear as people might think, and leaves the door open for any onscreen romance involving Kate to come from somewhere - and someone - else
* I've seen some speculation out there that Kate and Beth aren't identical twins here because they're played by actresses of different ages as adults, but there's nothing within the Pilot itself that suggests that the characters
aren't identical twins and so until/unless something comes along to explicitly confirm that they're not, I see no reason not to operate under the assumption that they are
* This isn't specified in the Pilot itself as aired (it might have been in the original script), but the day that Gabi, Beth, and Kate were knocked off the road was the day of Kate and Beth's bat mitzvah, and the necklaces that they were wearing were likely bat mitzvah gifts from either their parents or someone else
* I find myself wondering what the exact age difference between Bruce, Kate, and Beth is
* Having seen what the Pilot has established Mary's role as, I find myself wondering whether or not she'll actually ever learn that her stepsister and Batwoman are one and the same person (I'd previously thought it was an inevitability)
* Mary clearly sees Kate as being somebody to look up to, but it doesn't sound like the two characters are particularly close or have interacted with one another all that much
* Maybe it's the tenor of their scene together, but I really don't like Catherine Hamilton-Kane all that much, and don't think she actually loves or cares about either Kate or Mary, which creates an interesting contrast between her and the character she's clearly modeled after, Moira Queen
All in all, this was a very strong premiere episode that set up Kate's story pretty much flawlessly, and I can't wait until next week.