for Astral heron, if you are at a battlefield and get attacked, you play a spell and it resolves. then you let heron die. does your next spell still get the discount since the first was played while heron was at a battlefield? or not anymore since the heron has died?

Yes — your next spell still gets the discount. Heron's trigger condition ("when you play your first card... if I'm at a battlefield") is checked at the moment the trigger fires, not when it resolves (Rule 383.2.c). Once the trigger is on the Chain, the discount resolves independently of Heron — dying afterward, even in reaction, changes nothing.

So: first card resolves while Heron is alive → discount is created → Heron dies → your next card this turn still costs [2][A][A] less. Note the errata'd text adds "this turn," so if you don't play another card before the turn ends, the discount expires (Rule 317.2.c).