To answer your first question, you will have plenty of time to apply, you have until Dec 1st. Have your application ready to go when you get your scores back.
The second question, because you are not an automatic admit, your scores need to be high. I would think at least 1400+ (and that might be low). The nursing school at UT is very competive. If you are an URM, that will help your chances.
Last, make sure you apply to some other schools that you definitely could get in because you are in the top 10%. For nursing, TTU, UT Arlington and Texas State all have good programs.
There are lots of very good nursing programs in the state of Texas, do not limit yourself to UT. In fact, UTSA has a very good program, as does SFA. A&M has started a new nursing program. I am sure UT may be the pinnacle but you can accomplish your goals at many Texas schools.
Another thing I just wanted to mention about nursing schools. I spoke with a student who was trying to get into TTU’s nursing school. You do have to do prerequisite work and get a very high GPA to be considered for a nursing slot. She mentioned they were only considering candidates with a 3.5 GPA or higher. I believe Texas State also has a similar set up. Research these schools on their requirements to be accepted into the nursing program itself. Some of these schools might have a larger program (I’m thinking UT Arlington) that would increase your chances and/or reduce your stress in getting into a program.
@GTAustin Yes the other schools im considering are Texas A&M International or Texas State. Im not interested in attending UT Arlington, its just too close to home for me. My mother went through the UT Arlington Nursing program to get her BSN to MSN and Ive heard some good things from her. But personally, im not a fan of the Arlington area. UT Arlington is most definitely a safety school for me.