1. The new Wolverine in future movies will be this girl?
   There won't be any future Wolverine movies, this is it, at least for the foreseeable future.
2. Boy, the future for these heroes really sucks. They all die miserable deaths and bad guys still rule almost everything. What's the point?
   Yeah, the future for the X-Men has always been a bleak one in the comics, things do not turn out alright in the end for them. Such is life. The Uncanny X-Men, at least when it was written by Chris Claremont, rarely pulled any punches. In the series there's just too much for the X-Men to cope with, eventually something or someone is going to punch their ticket, it's just a matter of time.
   In the case of this movie,
   Logan
   , it appears as though Donald Pierce and his Reavers are the ones to have finally defeated the X-Men. It seems as though Mister Sinister may have had a hand to play in it as well (although he is likely to be the main villain in the next X-Men movie,
   X-Men 7
   , and he looks to be only a shadowy background character in this movie).

The New Mutants
is taking place in the 1990's, alongside the next X-Men movie (the currently untitled,
X-Men 7
). There will be characters crossing over from between the two movies, it's known that James McAvoy (Professor X) and Alexandra Shipp (Storm) are both starring, or at least co-starring, in
The New Mutants
for instance.

I'd suggest New Mutants could be set in the future timeline of "Logan" but then the X-Universe films would be set in THREE different movie time periods (past, present and future).
That would be a crazy decision by Fox. They would have a fixed timeline for their entire universe.

Even if that's Jean's funeral in the movie, it would still be nice to have her even in a flashback, since she's a big part of Logan's life.
While I certainly agree that Jean has been a big part of Logan's life, it would be more neat if they at least manage to show us Rogue with Logan, this last time, since she's the first mutant he has made friend with

1. I doubt there are going to be stand-alone X-23 movies, set in the far future where no X-Men exist.
   This movie just indicates that X-23 WON'T replace Wolverine in the X-Men films, since she exists in this futuristic universe
   You're right that X-23 would be living in the near-future, far away from the "new" 60s-80s cast from the current franchise. Then again, X-Men has never had a consistent (or even logical) timeline. They could find a way to sneak her in there or perhaps make her a part of the Deadpool franchise (which IS happening).
   However, remember that there are also plans to make New Mutants. I'm assuming Laura will be a part of that group. There's at least one other confirmed mutant in that line-up as of now: Wolfsbane, if the Maisie Williams story is true. I think Fox is actually thinking long-term for a change.
2. The point is to give Jackman a huge send-off and presumably avoid using the OLD X-Men cast (aside from Patrick Stewart)
   From what I hear, this is Patrick Stewart's last X-Men film as well. I think they're wrapping up the old franchise and are already in the process of wrapping up the "old/new" franchise that started with First Class to make way for New Mutants and Deadpool.
   Even if that's Jean's funeral in the movie, it would still be nice to have her even in a flashback, since she's a big part of Logan's life.

1. I doubt there are going to be stand-alone X-23 movies, set in the far future where no X-Men exist.
   This movie just indicates that X-23 WON'T replace Wolverine in the X-Men films, since she exists in this futuristic universe
2. The point is to give Jackman a huge send-off and presumably avoid using the OLD X-Men cast (aside from Patrick Stewart)
   Due to the lack of moderators, trolls can ruin the IMDB message boards. Don't feed them.