Possible Head Gasket or EGR Concerns

I am looking at buying a 3rd gen and came across one today that had the startup “rattle” then goes away 5 seconds later. I looked at quite a few videos including the car care nut’s videos on diagnosing and isolating but no videos talk about CEL codes appearing with either HG or EGR symptoms.

The car is a 2010 with 197k. The oil looked brownish, coolant looked full but cant rely on that as owner may be topping off. When scanning for codes, I got the following: P0300, P0302, P0303, P0304 codes. I personally witnessed the rattle at startup 3-4 times I started the car. Then its smooth. I have not performed the EGR / Putty knife test yet as I didn't want to get deep into the diagnosis as If it ends up being that the owner may decide to not sell it and i'm not there to help diagnose lol.

So my question is, would the misfire codes show up on both EGR and HG failures? Or only one of them or none or in both?

Any help would help as price is an as is sale for $2k.

 

Could you elaborate on why it wouldn't be just an EGR issue or just a HG issue or both, but adding it needing a whole new engine? Perhaps if engine is continually being driven with a HG issue, then I agree. I did see in another post titled "Death Rattle" by AncillaryRedoubt you state this:

"With a head gasket problem you won't get codes because the misfire does not last long enough. Which basically eliminates bad plugs, coils and injectors. This scenario virtually confirms a head gasket problem."

So I'm a bit confused at the diagnosis at that since this car has misfire codes. Also, I wrench on my own cars so at least save the labor part and those outlandish prices wouldn't apply to me. The more I see other videos the more I see similar issues to mine with different results which is why I'll be putting a borescope into the cyl to see for signs of seepage or washout and if a HG, at $2k may be worth buying and parting out lol.

Also, Booster is ok and HV battery was replaced 40k ago, He had the receipts from the dealer.