PlanetsCentral

The only reason to do a scedule change is to prevent the host from running. So if you did prevent the host from running change the scedule right away. This means you change the the scedule right after the hostrun you wanted to prevent on wednesday 12:00 if that was the last one you wanted to prevent. Which should in itself answer your secondary question.

So let's say usual hostrun is wednesday 12:00 but you wanted to prevent this one. Change scedule at 12:30 the same day. When the usual next hostrun will be at saturday 12:00 and that will be written in the game page.
Nothing else will change - there should not even be a need to change the auto checks. The host will still run if turns are in, and if there is a hostrun in that very time the hostrun at saturday will be delayed to next wednesday as usual because you want to prevent a host from running at saturday 12:00 when the last host ran friday evening due all turns were.

No. If I did that, host would wake up at 12:30, look a little confused "whoops, I'm on a 12:00 wed/sat schedule, I must have forgotten the Wednesday host", and will run a turn. The scheduler must be able to deal with delayed hosts. Hosts can be delayed by other hosts running at that time, general system load, unplanned reboots, etc. You wouldn't want to skip a host because it was delayed by a few seconds? There needs to be a grace period. Right now, that grace period is set to 6 hours for most games.

Thus, the "pause end" time needs to be after the grace period. There is some pretty complex logic there to try to do the "obvious" thing. Setting the "pause end" time precisely on a host date makes everything clear.

I really think that feature is what is causing so much trouble here because that's the reason for the host to run sometimes right after scedule changes and sometimes not. Which makes perfectly sense afterwards yet is practically impossible to predict.
(but naturally we want to keep that feature and just make the next host run predictable from the game page)

It's actually simple: host runs at the schedule change time unless the host before was too close. "Too close" means: after the previous host-that-would-have-been. For a Thu/Sun schedule starting Sunday, the Sunday host will run if the previous all-turns-in host was on Thursday or before. This condition applies all the time: a scheduled host will run unless the previous all-turns-in host was too close.

Again, the logic is not easy, and the best way to get out of the situation is to let the computer to it and just show the next host run.

--Stefan