Multiple Codes

A few days ago my 2010 started throwing multiple codes and gave me a "Check Hybrid System" alert, then shut down. After letting it set for a few minutes I was able to limp it back home. It started off with the engine running then shut down and I coasted in on electric. Had multiple codes as follows:

P0300
P0302
P0304
P261B

I'm not worried so much about the cylinder codes right now, as they aren't the ones shutting the engine down. I've known for a while that I've had a couple rough cylinders on start up but then it smooths out and runs fine. Troubleshot the P261B all I could and decided it must be the pump. Installed new pump today and ran in maintenance mode for 30 min or so. Ran perfect with no codes at idle. Before it could only idle a short time before it would throw codes again. Put everything back together then went for a drive down the street. Made it about a mile before I got a temp light. Thought maybe I didn't get the reservoir all the way full so I stopped in to get some more coolant. When I came back and started up I had the "Check Hybrid System" with the 261B code again. However this time I got a 261C code as well. That one had never showed up before. All the cylinder codes were back as well. Despite not ever showing up during the maintenance mode ops checks. Not sure what to do next. What exactly is the computer monitoring to think there is an issue with the coolant pump? It doesn't give me a temp code or warning before it throws the "Check Hybrid System". So it seems like the computer is designed to shut it down before it will get hot enough to throw the temp warning. As an aside, I don't get hot air out of the heater, despite it being the middle of summer. It's like the heater core isn't getting coolant to it. Which is part of what made me think getting a new pump would fix the issue. Any insight is greatly appreciated.

 

255k. Had it for about 6 months. Problem free until now.

 

Turns out, it was indeed air in the coolant system. I had bled the system for about 30 min while I put everything back together. I assumed this would be enough time. However a few hours later I bled it again and got a ton of air out of the system. Topped off with coolant and drove around a bit. Been problem free and hasn't popped any codes since. Thanks for everyone's help!