Thank you for reporting this. I have indeed neglected to test the mod with disabled stations.
I have been able to reproduce and fix 2., but I am not able to reproduce 1. On my different test maps, when a train is waiting at a station after being dispatched and the station has its state changed to disabled (via signal), when the train finally leaves the station its schedule is updated accordingly (station removed from schedule, exactly as for enabled stations).
Could you maybe detail a bit more what is happening in 1., or maybe share a map so that I can reproduce the bug?
Also, be careful with disabled stations. If a train is dispatched to a station, and the station gets disabled while the train is en route, the train may be stuck on the rails if there is no path to the next station from where the train is stopped.
Again, thank you.