Prosecutors are not in the business of dismissing cases. They're there to prosecute and to do otherwise goes against the grain. If the complaining witness wants to see a charge dismissed, then he should absolutely work with the defense attorney. Obtaining a dismissal is often counter-intuitive to the lay person. The complaining witness may present a lot of reasons for wanting a charge dismissed that end up unintentionally bolstering the prosecutor's desire to continue to prosecute.
Possible, but not likely. More likely that you're seeing what one frequently sees: An inefficient bureaucracy. Likely every bit of investigation was done on this case the day you were arrested. There's really no good excuse for it taking more than a few days to get the case filed, but this happens all the time.
I handle a lot of these civil demands, typically in conjunction with criminal theft charges. $275 is excessive. Can they sue? Yes, the law allows it. Will they? Very unlikely. They're hoping that for the price of a postage stamp you will send them $275. More than likely the letter you received is from a firm in New York, California, or Florida. Do you really think they're going to come to Texas and sue your daughter over a petty theft? What jury would award them much if anything? In my...
If you had a true pre-trial diversion, then you ultimately will be able to have the matter expunged and not just a non-disclosure. Expunction is much better that non-disclosure. With an expunction, all records are deleted and/or sent to the court that orders the expunction. Under this situation, you'd have the right to retrieve those records and do with them what you wish. If you did not retrieve them, then they would be destroyed by the court after a year. In this instance, yes, the statute...
If you were convicted or even put on deferred probation for class a misdemeanor assault against a family member, then you're not legally qualified for an expunction or an order of non-disclosure, short of getting a pardon from the governor.
You should be out shortly after midnight on Sunday. That is to say, as soon as the clock goes from 11:59 PM, Saturday, to 12:00 AM, Sunday, the jail will give you credit for that "day," and start to process your release. It is unlikely that you would be able to qualify for something like inmate worker in such a short amount of time.
P.S. A much more important concern should be the proper resolution of the criminal case. Because it is a class-c misdemeanor, if you can resolve it by deferred adjudication, then you may later file a petition to have the matter expunged, which I highly recommend.