Can I disable transitions and animations system-wide? I liked the transitions (fade-in, fade-out, sliding) and animations (when switching pages, or apps) when I did not know them. Now, I´d like to disable them everywhere. Is that possible? Is there an app for that? Could an app at all do such a thing?

Good example is: 

Lock the Ipad. The screen fades out. 

Switch it on -- screen fades in. 

Gimmicks like that annoy me meanwhile. Imagine an Ipad that boom! just shows the locking screen, and does not fade it in. I'd prefer that meanwhile.
I think your only option is to Reduce Motion, or perhaps turn off Transparency [which will speed things up but not affect transitions themselves.]

Jailbreak may give you more options, but I've never tried that.

Reduce Motion

Turning of Parallax on older devices can help improve performance, it stops motion effects in the home screen and in some other parts of the system. Switch this off in Settings>General>Accessibility>Reduce Motion. Tap to turn Reduce Motion on (green).

Transparency

Turning of transparency may help, though it the OS won't look as pretty. You can turn it off in Settings>General>Accessibility>Increase Contrast>Reduce Transparency>Switch to On.

Source: How to improve iOS 8 performance on your iPhone or iPad