Does somebody know whether there are hidden preconditions for prestige classes?
And if so: is there any place where one can check them?

I have repeatedly checked that characters meet all requirements for a prestige class, and the only one that in fact is offered then is the Arcane Archer. All other prestige classes are locked behind something that I can't work out by myself.

The same seems to apply for spells. Some spells are even given automatically like the Allies for Ranger, and then they can't be used because they have [0/0]. What's the point of...?

The highlighted prestige classes are well available.
Using Mystic Theurge on my casters right now without any hitch.

Think you're just missing the skill prerequisites, which need to be met BEFORE any attribute modifications.

Thank you very much! That works :-).

It's hard to work out such things without any hints... in fact I assumed that "ranks" should be the values that are given as "skill values" in the character summary.

Is there any ruleset documentation where I could check some other things about the games math? The SRD does not cover that part as far as I see.

Pretty much the only resource for this game I know of is the Guides section over on Steam.