Yes the background check for guns is the same in every state
Yes.
No
yes
Yes
Depends on Texas law.
Texas, the state of your residency
Only if you're having it transferred to an FFL licenced dealer in Colorado (the most you should have to pay for receiving is $20 - $25). You could buy a long gun in Colorado or any state bordering Colorado - unfortunately for you, Arizona does not.
Federal law is 18
No. You need to buy auto insurance in the state in which you're legally resident.
Long guns, yes. Handguns and NFA items, no.
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.