As long if he/her has a licence.
Nowhere in the US.
Long guns, yes. Handguns, no.
yes
Yes.
Texas, the state of your residency
Yes... I may be wrong about this, but I believe Delaware is one of the states where you must be a resident of that state to buy a firearm from there, although I could be wrong about that.
Yes- but only from a dealer. You may not buy a firearm from a private seller in ANY state other than your own.
No. You need to buy auto insurance in the state in which you're legally resident.
To possess a gun or buy ammo in Illinois, a resident must have a Firearm Owner's Identification Card.
Yes the background check for guns is the same in every state
If you buy it in Texas then you will be liable for sales tax. Otherwise no other taxes should be levied against you.