You cycle pillar and hand, and once they're on cd you spam AAS, space bar combos, or run for your life.
I'm the only Dainn who uses spacebar combos as far as I know >_>;
Another thing to note: Ice Arrow (15 mp at level 1) to get a recharge
So in this case, Dainn is much more able to regen mana, even when under the amount for Fire Orb. I'd say Eir's melee limit should definitely get bumped up for balance purposes.
As for tourney rulesets, TFT didn't even take a serious look at user suggestions on their official forums =/