You really need an attorney. You have too many procedural questions to handle this on your own. You just can't get all the help you'll need from blogs and web sites like this. I am very familiar with the courts in Denton County and can assure you that they will not cut you any slack just because you are representing yourself. (Her either, by the way)
Her failure to provide you with a copy of her answer is not fatal to her case. You are not entitled to a no-answer default for that reason alone. If she filed an answer, the court will hear her side of the story.
If you two can reach an agreement, you can both sign an agreed order and there will be no reason for a trial. If you cannot agree, then, yes, your hearing goes on the contested docket. Before you race to trial, you should consider mediation. You can get inexpensive mediation in Denton County and at mediation you don't have to follow all the procedural and evidentiary rules that you have to follow at trial.
If she will not agree to medation, you can ask the court to order mediation by filing a motion for mediation, setting the motion for a hearing (giving her at least 3 day's notice of the hearing), and asking the court to refer you to the Denton County mediation service.
I completely agree with Mr. Daley, especially when it comes to getting an attorney to help you. If you try to handle this on your own, then fully expect to be held to the standard of an attorney. So, if you miss a deadline, don't know the rules of evidence and civil procedure or better yet, the local rules; then you are possibly jeopardizing your case. I wouldn't risk it.
Also, in regards to the mediation - many judges require the parties to mediate before you can even set the matter for final trial.
Best of luck.