1) there is no IV/PID relation, if it has one it is indicative of a generated one.
2) correct, the egg PV is set in one RNG, and the IVs are set through another after inheritance.
3) pretty much.
4) see 1, there shouldn't be a relation. Having a 32^6 chance of getting that IVPID relation is WAY too low to be "legit".
5) If you can't get the egg PID on a reasonable frame (IE below 4000 eggs) on a particular seed, it's probably hacked. Checking this is so laborious nobody does it.
6) They aren't generated the same way. There might be a relation this generation as the PID and IV inheritance is generated from the same process, as opposed to IV+Inheritance last gen.
As Codr said, it's OCD.