Have you ever been working on a story, you know the shape of it, the currents running between the characters, where the eddies and rapids ought to be, and you're banging away at it...and it changes?

YES. I admit I'm brand new and supremely naive about this writing thing, but I have read interviews with authors where they say the characters "spoke" to them or had minds of their own and....yes.

For the abrupt ending...is there a way that you can continue without making the next paragraph the very next thing that happens? Maybe jump forward in time, or put a frame story around it, or switch to another characters POV? Or it could be that your ending is fine. Maybe you've said all you need to say.

I find shifts in mood/tone more problematic, because it seems my narrative voice changes when I write at different times. It can be hard to keep the tone consistent throughout the fic (unless you're lucky enough to be able to finish it all at one sitting). In that case I tweak what's already there instead of writing new stuff, and often I fall back into the rhythm. But it's scary--I presume professional writers have REALLY good control of their voice and style to make it all the way through an novel without changing midstream.