2010 Corolla ac blower and blinkers went out

Has the battery light come on? If so your alternator is bad. Have the alternator checked out.

Nope. No battery light. Alternator was just replaced a couple months ago

I would think your blower motor is bad or the blower relay is where I'd go with my focus. The relay is cheaper obviously I'd go that way first. No, I doubt the tran has anything to do with engine light. your blinker goes out because the relay quit working for you. Probably a round device, a bit small and in the power box. All it does it shut off current on the circuit so that the light goes on and off with a sound of tick tick. That is what you are hearing during turns. Simple things in life.. good luck. ( if it was me, I'd put very little money in a Corolla and go get my parts out of a junk yard.The yard I go to rotates cars out every 5 weeks. I'm always getting new parts off cars as I need. Life is good.