does abandonded hall choose Irelia, meaning you can then use the legend

Yes. Choosing Irelia for Abandoned Hall's effect counts as "choosing a friendly unit," so Blade Dancer triggers and you may exhaust her and pay [A] to ready Irelia (FAQ #10297).

The choice is made when the Abandoned Hall trigger goes on the Chain, so Blade Dancer's trigger stacks on top of it. When it resolves, you ready Irelia — which also triggers Irelia, Fervent's own "when you choose or ready me" ability. So the full payoff is: +1 from Abandoned Hall, +1 from Irelia's "chosen" trigger, +1 more from her "readied" trigger, and Irelia untapped.

One caveat: the player choosing is whoever played the spell (Abandoned Hall's ability is controlled by them, Rule 190.6.c). Only that player's Blade Dancer triggers, and Irelia must be a friendly unit they control at Abandoned Hall.