You can be and will likely be arrested on the spot. If you had a payment plan and defaulted, and a warrant was issued, then you would be the proud recipient of a Capias--warrant issued by the prosecutor. If you walk in without having addressed them first, Expect that they will arrest you at that point.
I would think this is a definite possibility, but I am a California attorney & not knowledgeable with TX laws. You should immediately consult a local TX attorney before you do anything further - call an attorney ASAP
This is not intended to be legal advise or as legal representation. I am a California personal injury attorney . Be aware that every state has its own statute of limitations; and statutes & case laws that govern the handling of these matters.
Probably. There is no reason that they shouldn't arrest you. Check on the warrant status of your other ticket. If it's in warrant clear it up and then go.