A busted hazard light switch, which is located on the multifunction switch, will also cause the brake lights to not work. But just the two outer brake lights. The center brake light will still work.

As for the heater blowing cold air, try flushing the heater core, as outlined here: https://blazerforum.com/forum/showthread.php?t=18868

It's very easy to do, shouldn't take more than 10-20 minutes.

Hope this helps!
-- Kevin