I know there's a technical term for what's going on, but I'm no emulation expert. Basically, I enter the second level and immediately experience a much greater animation speed, which almost makes the game unplayable. The sound and music is the same. I definitely did not tinker with any of the options between levels.

I imagine I'd have to go into the .conf file and change a figure or two, but any advice beforehand would be much appreciated.

As mentioned here few times already, you can try changing core to "auto". Maybe it'll just work. But I think this issue is not emulation-related. I vaguely remember encountering it ages ago, when playing Raman natively in Windows 98. Sometimes timer went crazy and the game ran as fast as your PC could handle.

Good news? It wouldn't stay that way. The game just needed to reload some stuff and then fixed itself. Bad news? Easiest way to do this is to restart the level, which means losing a life.

If that really doesn't work (it sounds as though you already tried a few times) you may start messing with graphic settings in the game itself. You need to enter OPTIONS right from main menu, otherwise some options won't be accessible.

You need to tweak a bit, but your computer should be able to handle full settings with PCI1 (the most advanced graphics driver). Maybe if you play with smoothness and/or framerate, you can get better results, but you need to see for yourself :)

I found out that if the game does that, then go to the game's options, and change the frequency from 60 to 50, then just put it back to 60. The game will be back to its normal speed.
My problem with the game is the saves. It just doesn't save up to the last point. I go back and i find that it only loads up to my previous save :P. Losing medalion thingies

Vista/7 + UAC + something trying to write in Program Files = Weeeeeird stuff happening.

If that's your case, simply install the game somewhere else, eg in C:\Games. You'll probably find your saves deep down somewhere in Local AppData (most probably "C:\Users\username\AppData\Local\VirtualStore\Program Files"...)
I'd presumed that GoG team had already resolved those issues, but yours certainly sounds like a Virtual Store problem.

Well i found out that is you start the shortcut with admin privileges, it also works and saves as it should.

True :)