dumb questions/musings about agility

Hullo I am new here and this is the first forum at which I haven't first lurked for five years before posting. i just found this place yesterday! huzzah.

this forum looks very nice.

questions came into my mind today when I was thrown repeatedly into battle with Magic Urns. Wakka had some auto-regen armor and immediately when the encounter would begin, i'd see flashes of several hundred HP that Wakka regen'd in, like, half a second, before the battle menu even showed up. then i tried going into battle with an Urn when Wakka actually did have low HP, and i found that his HP went up about 500 HP in the blink of an eye.

so, questions- does this have something to do with the fact that Urn never attacks (besides counterattacking)? or is it that Urn has an incredibly low agility stat? (i looked it up...yeah, his agility is 1.) does an agility stat of 1 effectively mean the character/fiend never attacks (again, besides counterattacking)?

i know regen works after every tick. so in theory, shouldn't regen be more powerful (cure you more often) the faster a character is? doesn't higher agility = more ticks? or does it depend on the difference in agility between the character and opponent(s)? i've only ever seen this jump happen with the Urn.

excuse me if these are silly questions i am just sad that ffx is over as i play endgame content to excruciating completion