Does this mean the heir has to be the household member that "makes the phone call" or "uses the computer" to make the purchase? e.g. Could Thornton Wolff complete this for the 1st heir on week 1 day 1?
It's really more of a household thing — each household needs to make those 2 separate purchases, so I don't care who makes the purchase. I may have said heir in the rule, but it does not matter.
Do these have to be unique for each heir or could each heir potentially purchase the same building and property?
They need to be different as in the Immortal Dynasty. Switching active households after moving may indeed allow you to purchase the same property again. I'm not sure on that. But, just think of it in terms of logic — it doesn't make sense if you can do that, so don't do it.
Would some/one of the NPCs joining the household affect requirement #2?
If an NPC becomes a household member, then they're no longer NPCs. So, yes, it most definitely affects rule #2 — you need 10 NPCs at the time the heir is to move. All of those would have to be outside the household. You're free to bring NPCs into the household, no problem. But, that changes their status.
Do the 10 Best friends from requirement #3 have to be non-household members? If so, could they have previously been a household member?
I'm not quite following you. When the heir is ready to move examine the relationships of all household members. If you count up 10 different Sims that are Best Friends (household members are fine) you're fine. Clear?