If I have a heron on a battlefield and the opponent has an irelia on the same battlefield, and I've already played my first card this turn. Then for my second card I play Back-off on irelia, does astral heron also pay the deflect cost or do I still need to pay a power cost for irelia deflect?

Yes — Astral Heron's discount covers Irelia's Deflect, so you don't pay any Power for it.

Back Off's total cost is 3 Energy base + [A] Power from Irelia Fervent's mandatory Deflect cost (Rule 809.1.d). Astral Heron's pending discount ([2][A][A]) applies to your next card's combined cost — including additional costs, which can be reduced all the way to 0 (Rule 356.4.f). So the [2] brings Back Off to 1 Energy, and the [A][A] wipes out the [A] Deflect cost. Total: 1 Energy, 0 Power.

Same interaction as Astral Heron + Repeat costs — the discount reduces the whole card, not just its base cost (FAQ #11670).