My name is XXXXX XXXXX I'd be happy to answer your questions today. Is he arrested right away?
It depends. If the story told by the child is sufficient to convince the police that there is probable cause
to arrest the teacher, they have the option of getting an arrest warrant and going to pick him up right away. They can also choose to wait, investigate the allegations a bit, and then pick him up when they have more evidence.
Are there depositions or a trial, and in what order?
If he's disputing the charges, it'll have to go to trial. Depositions are more common in civil cases, but may be taken if there is some reason that it's necessary to preserve testimony for trial - one example is if a prospective witness is deathly ill. They'll take a deposition in case he doesn't make it to the trial.
Is he placed on house arrest if there is a trial?
If he's on trial for a sexual act against a child, there's a good chance that he'll remain in jail pending trial. Bail is typically pretty high on such cases.
Does he or the girl have to testify at the trial?
As a criminal
defendant, he has a Fifth Amendment right to choose not to testify. The Sixth Amendment gives him a right to face his accusers, so the child will probably have to testify at trial, yes, and will be subject to cross-examination.
Is there an out of court settlement from the district?
An out-of-court settlement from the district wouldn't have any bearing on a criminal case. If the child was also suing the school district for somehow putting her in a position where the attack could occur (such as not checking the teacher's background), then it is possible that such a case would settle out of court in order to minimize the publicity.
Are there restraining orders.
There probably would be a restraining order preventing him from contacting the child, yes.