The petition must be filed in district court for the county where the arrest or alleged offense occurred. For the specific procedure, see Tex. Code Crim. Proc. Art. 55.02.
At least $207 and typically about $250 in district court, plus $28 fee for petition for non-disclosure. See Tex. Gov't Code § 411.0745.
The person is not required in any application for employment or licensing to state that the person has been the subject of any criminal proceeding that is the subject of the order. Tex. Gov't Code § 411.0755.
There is no statutory language regarding a waiting period.