It looks like you have to begin a new game and make a new collection of saves every time an update comes out.
Saves hasn't really been broken for half a year or more, this time it sort of happened and I've pasted a way to make it work (sometimes) in OP. If that's not enough then stop playing unfinished games, that's just how things go.
Either some saves are due to changes broken
Yes, a game in development will change, sometimes that means saves break.
or the skip option is gone
Has never been the case in my game.
so you are stuck in the same day.
Also never been the case.
If the college part was not such a boring grind, it would be only half bad to begin a new game, but...
Have you tried faster mode, because it sounds like that more your speed.
All of this information is in either OP and the ingame tutorial. But if you don't bother to even look then maybe it's not the game for you.
I also assume that the skip option you're referring to is to forward time, you can do that by clicking on the clock in the game. This has been the case for several updates, this can also be found out, as mentioned above, in the tutorial.