Tamara is right, the crime is lying on form 4473.
It is still an illegal straw purchase even if the person you're giving it to is not a prohibited person (because again, the crime is lying on the form).
It seems in OP no form 4473 was ever used and thus this is not a straw purchase.
so to answer:
1. Not a straw purchase. Star purchases can only happen when a 4473 is involved, which is only involved when dealing with an FFL.
2. Doesn't matter who pays for it because you're not dealing with an FFL. If you were dealing with an FFL it matters very much who pays for it.
3. If dealing with an FFL this would be the best course of action, but again, no FFL here.
4. State laws apply
I am also not a lawyer.