As for GTA, I'd have to go look at the Arkansas criminal code. I'm pretty sure that "GTA" goes by some other name here.
fullsize only, one of the first things that I learned in law school is that the devil really is in the details. I can't give you a hard and fast answer with the examples that you've given. For one thing, the examples you've given involve something more akin to a citizen's arrest, rather than an SD shooting. There's a different legal statute for defense of property, Ark. Code Ann. 5-2-609:
A person is justified in using nondeadly physical force upon another person when and to the extent that the person reasonably believes the use of nondeadly physical force is necessary to prevent or terminate the other person's:
(1) Commission or attempted commission of theft or criminal mischief; or
(2) Subsequent flight from the commission or attempted commission of theft or criminal mischief.
Note, however, that it refers to NONDEADLY force. Is shooting out a tire "nondeadly?" Off the top of my head, I don't know.
As for stopping a violent carjacking by shooting the carjacker, again, the devil is in the details. Let's say that I know that there's only one person in the car, and that the carjacker shoots the driver in the head, instantly killing him, hops in the car and drives away. Can I reasonably believe that the carjacker still presents an imminent threat of death of substantial bodily harm to the driver? Compare that to a scenario where I see a "Baby on Board" sticker on the car and hear crying after the gunshot. In that case, can I reasonably believe that there's a baby in the car and that the carjacker poses an imminent threat of death of substantial bodily harm to the baby?
sigcurious, if you'll read the retreat section carefully, you'll see that, when it comes to defense of a person, there's not much of a duty to retreat in Arkansas:
5-2-607. Use of deadly physical force in defense of a person.
(a) A person is justified in using deadly physical force upon another person if the person reasonably believes that the other person is:
(1) Committing or about to commit a felony involving force or violence;
(2) Using or about to use unlawful deadly physical force; or
(3) Imminently endangering the person's life or imminently about to victimize the person as described in § 9-15-103 from the continuation of a pattern of domestic abuse.
(b) A person may not use deadly physical force in self-defense if the person knows that he or she can avoid the necessity of using deadly physical force with complete safety:
(1) (A) By retreating.