2012 P0300 P0301 P0302 CEL ON

Of course, feel free to take 10 minutes to check the pipe. I refer to cleaning the cooler.

 

Not exactly DIY, but a leak-down test is commonly used. One at a time the cylinders are set to Top Dead Center on the compression stroke, an air hose connected (basically a pressure hose without the valve), a special leak-down guage set is connected, and then compressed air is supplied. The behaviour of the gauges, and just observation, help diagnose what is leaking and where.

Even without the special gauge set, just doing the above and ovbserving, you can diagnose quite a bit. You're looking for air leakage, and where. For example, if there's bubble in the coolant reservoir, you've got a leak between cylinder coolant passage.

He has problems with his gauge set here, but still informative:

 

The code p0300 is random misfire, and p0301/p0302 indicates misfire on cylinders 1 and 2. This is becoming classic third gen head gasket failure codes. The head gaskets fail between cylinders 1 and 2. Maybe due to the introduction of EGR gas at the other end, the cylinder 4 end of the intake manifold?

I wouldn't. You're just getting a short reprieve, and messing up everything the coolant passes through. FWIW, that cr@p can apparently be flushed out with a 50/50 white vinegar/what solution.

 

You’ll lose everything in the seal’s path; it clogs leaks and then regular open passages that needs to be open for flow.