Yeah, max dex bonus rule still applies, regardless of whether or not you have the appropriet armor competency. Ditto for the
speed reduction
Something about makes an (first three letters of "assume") out of (next letter of assume) and (final two letters of assume).
Spell failure comes from the armor getting in the way of gestures, and doesn't apply to all spells (just those with gestures - called somatic components in the spell descriptions) so even a wizard casting Arcane spells could wear full plate + a tower shield, and have some spells avoid failure (or almost all, with the Still Spell feat).
With Psionics, all you do is stand there and concentrate. You don't have to move at all.