Advice Needed! P0401, P0300, P0301, P0303 Head Gasket and/or EGR?

Prius 2010 Base; 188K Miles. Bought with 80k Miles from original owner for cheap because it had bad/noisy wheel bearings. Replaced front struts last month. It has been using some oil lately (less than half a quart every 6 months). Other than that, no issues whatsoever.

We were going on a camping trip 100 miles north (uphill). 40 miles out I noticed a red light flash for a few seconds on the dashboard, asked my wife to look it up (never seen a red light on the dashboard before). I decided to pull over just in case and I'm glad I did, it was the high temperature warning light. As I slowed down to park on the side of the freeway I noticed the CEL turn on for a few seconds. No other problems besides the lights at this point.
Once safely parked at the side of the freeway I let the engine run for a while before turning it off to check the engine bay for any issues and double checked the fluids. Nothing seemed off, oil, coolant and break fluid levels were all fine. Looked under the car for any leaked fluids and nothing, just condensation from the ac.

Started the car again and as soon as the ICE turned on the car started shaking really bad. Decided not to risk it and got it towed (flat bed) back home. I checked all fluids again and they are at the normal level. Turned the car on and it wasn't shaking any more, no warning lights either. I started driving it around the block and as soon as I started accelerating it started to shake again and the CEL started flashing so I turned back and parked it on the driveway where it is waiting to be repaired.

When I was troubleshooting the issue that turned out to be faulty struts/shocks I read a lot about the EGR and I was planning on taking out the EGR components in November (when the weather is nice here where I live) and giving them a good clean. Now, I'm not sure if the head gasket needs to be replaced so I turn to you guys for help.

1.- I'm leaning towards a bad heat gasket and a clogged EGR system, just a clogged EGR system or a clogged EGR system and bad MAP sensor. Would you guys agree? Am I missing any other possible causes?

2.- What would be the best (most definitive and easiest) way to know whether the head gasket is leaking/bad? Not sure I want to fix a bad head gasket, might just replace the whole engine or sell the car for parts.

3.- If it was your car, what steps would you take in finding the fault? (I pulled the codes in the title of this post with my friends scanner, planning on buying an Autel AP2500 tonight).

Thanks a bunch for the help!