Triangle! + Check Engine

First, a basic, general question:

Where are you folks getting the these trouble codes, like P0AFA, P0301, P0302? I gather you must have some sort of gizmo you're attaching to the CAN bus to see the diagnostic codes that Toyota only wants dealers to see?

Second, Problem description:

2009 Option Level 4 (I think) Touring, 116Kmiles, well-maintained:
First symptom: 3/4ish-second beep upon powering down. Persisted for several days; first couple times I thought I was just imagining it, but no, definitely not.
Second symptom, yesterday: Air conditioner seemed to cut out on my way home from work. By the time I got home, I could hear the air conditioner motor cycling, so it either had come back or some other part of the air conditioner was failing. However, this morning, it seemed to be working fine.
Third symptom, today, driving on freeway: Master Alarm (triangle!) + check engine + VSC. Pretty sure the air conditioner cut out again too. Pulled over, powered down. Checked fluids; all fine (although radiator coolant is kinda hard to see for sure). Perhaps most relevantly, inverter coolant level is fine. Powered up again: Triangle! + check engine, no VSC light. Timidly drove home and rented a car. Beyond the warning lights, it's not obvious that there's anything wrong with the car; no loss of power or odd noises, for example.

I'm guessing, but I'm not sure, that the first symptom is what you folks mentioned elsewhere: The key fob battery being low. I replaced that battery, and it may or may not have solved that problem, but it didn't solve the big problem.

Any suggestions?

 

OK, thanks. Probably not the 12V battery; I had that replaced ... I think around 90Kmiles or so.

 

Oh, I also checked that the gas cap wasn't loose, since I'd heard that that can cause the Check-Engine like to turn on. It wasn't.

 

Ah! That sounds like a very good suggestion. Thanks!