This answer depends mostly on whether Texas wants to pay for your extradition. The state that orders the extradition has to pay for the transportation of the inmate being extradited. Generally, the severity of the crime is the largest factor involved. If you have a long criminal history, or someone was injured in your felony DWI, if your case was notorious, or if the state decides they want to pay for extradition, the state might favor extraditing you back to that state. There is no way to really answer this question in a concrete fashion. There are so many factors that go into the decision. I would say that the lack of state funds and the recession we are experiencing would help prevent a state from fitting the bill to transport you all that way.
Essentially, it would be up to Texas.
If you are violated on your paper, the warrant for violation of probation would most likely have the area of the United States where they would extradite from. If you get arrested in the other states for something, Texas may not want to bother if it is new petty offense. You also would need to check with probation to properly move your probation back to Tennessee through the interstate compact. You should speak with a lawyer in either Texas or Tennessee, depending on where you are currently living.
Yes. If you're on probation in one state, and get arrested for any offense in any other state, you could get extradited back to the probation granting state. Sure it costs the state money, but don't believe that they won't do it. You're on probation, make sure you inform your probation officer and obtain permission from the probation court before you move. You need to transfer your supervision to the state you are moving to. It's the first rule on your probation order, don't engage in illegal activities. You're on probation, don't get arrested.