Yes, if the conviction was for felony DUI. In a few states, you must have a state permit to purchase, and some states may withold that permit for a recent DUI. However, we do not know what state you are in.
An arrest if no charges are filed may not prevent you from buying a firearm. You cannot buy a gun after a plea of guilt or finding of guilt for a domestic violence related offense even if just a misdemeanor.
So long as you may legally possess a firearm, no.
A DUI is not a disqualifying offense for owning a firearm.
Yes, if you were convicted of it. It's a felony charge.
No
You need a lawyer to get a correct answer.
DROS is Dealer's Record of Sale. That is identifying information on you and the firearm.
A DUI does not normally prevent one from becoming an attorney. If there were other criminal charges associated with a DUI, it could.
You need a lawyer for a legal and correct answer.
Yes, it will.
No. DUI is a crime because it shows an "I don't care if I kill or injure someone else by my carelessness", and such people should not be armed.
A DUI is unlikely to prevent an American from getting a UK visa.