Do any or all of the skills have a cap? In the manual they seem to be represented as percentages, thus implying a potential cap of 100.

Yes, skills are capped at 100% according to the RPGDot Guide; attributes are capped at 23. There is also a level cap at level 10 but you might not reach that, depending on how you play.

I can clarify from experience that 23 is not the stat cap, I've increased Mental past that significantly and every time I increase it my mana and related skills are boosted as well.