Does the use of AE damage through Brood Chamber or Heavy Venom Cannon allow it to ready when destroying an enemy unit?

Also just to make sure, does the AE damage of any combination of Brood Chamber(s) or Heavy Venom Cannon(s) stack?

Area Effect is not an attack, so no.

And AE damage does stack. Keywords stack only where they include a numeral such as Area Effect (2).