There have been various discussions as to whether doing a web check-in changes your chance of an upgrade with no firm conclusion one way or another.

I tend to side with the view that if you've checked in online, the airline can be more confident that you will travel and may upgrade you based on this. Someone who hasn't checked in may turn out to be a no show and if they are upgraded in advance then more work is required if/when they don't turn up.

Regarding your second flight, if it's on the same PNR as your first, then you will be able to check in at the same time as your first, even it's > 24 hours to take off. This is certainly the case for me although my time differences are not as large as yours.