A creature that is both a Beast and a Bird still only gets one instance of ward {1} from Radagast, Wizard of Wilds's first ability.

If Radagast, Wizard of Wilds is a Beast or a Bird, it will have two instances of ward {1}.

Radagast, Wizard of the Wilds's last triggered ability will resolve before the spell that caused it to trigger resolves. It will resolve even if the spell that caused it to trigger is countered or has otherwise left the stack.