Aether, here is my understanding of your bolded words... kaphotics can correct me if I'm wrong (he's brilliant)
ID Legality- Somewhere in the bowels of the game's program, something spits out your TID (Trainer ID that you see on your trainer card) and SID (Secret ID, which is invisible to the player and keeps to people with the same TID from being considered the "same" trainer). The odds of two players having the same TID and SID is something akin to being struck by lightning and winning the lottery on the same day. Personally, ID legality is something I don't know how you check yet.
PID/IV relevance- Anyone with AR can overwrite IVs, EVs, Shiny status, etc. Just because you overwrite the values doesn't mean it will be legal in game from a checker's standpoint. Specific IVs, natures, and genders are all tied into a pokemon's PID (Personal ID that you will never see ingame). When you overwrite with an AR, versus actually taking the time and using the programs to find out which PID will generate the nature/IV/gender you want, you will appear hacked very quickly. This is why a lot of people who traffic in "hacked" pokemon raise flags... they just change a few numbers, but nothing with the PID. As kaphotics said, when it comes to non-shiny eggs-based hacks, IV is not related to the PID. All you have to do is find a PID with the nature/ability/gender that matches using a program called RNGreporter. Finding the right PID for shinies or wild pokemon is a little more difficult. I believe Pokegen has a built-in feature that will find an applicable PID if one exists.
Sync checks and encounter slots, someone else will have to answer.