Ive heard that this is possible in Texas
Your parents designate where you live until you are 18. If they designate the place you have chosen, that should be fine. They are still responsible for making sure you are supervised appropriately and have the things you need, for that reason most parents require their kids to stay home until 18.
Before you move make sure you have as much education as you can get (at least your GED or high school diploma). It is much easier to find a job with education. Some college helps a lot.
This answer DOES NOT establish an attorney-client relationship. This answer is based on the limited information provided and is not intended to be conclusive advice. There are likely other factors that might influence or change the advice after a more lengthy consultation.
Only if your parents agree. Otherwise, no. I'd point you to my blog post about this, but AVVO won't let us include links to our own blog posts any longer. If you Google "Emancipation of Minors in Texas" my article, which explains this in detail, will be one of the top results you find.
That would make you a runaway unless you have your parent's permission.
This does not establish an attorney/client relationship. Dallas, Denton, Collin and Tarrant County, Texas practice area. Principal office located in Lake Dallas, Texas.
You say "unemancipated" but you're trying to make decisions on your own and just expect your parents to deal with it. If you want to go through the emancipation process then you can look up the law and steps necessary to achieve this, like how to show that you're financially stable, self-supporting and responsible, then a Judge can decide if you are well enough on your own to emancipate you. However, this process will likely take until you've turned 18, so try to follow the other attorneys advice here and get parents consent for your decisions before you're cast as a runaway. Even joining the military before 18 takes parental consent and likely a GED/High School diploma.
Hopefully you're not going back to an abusive or dangerous environment with your parents, but that's a bigger topic that you didn't hint at in your question so I won't go into it.