Yes, the database is stored on your computer at all times. I have downloaded the trial version and installed it and I have found the MDB file in the installation directory:
Database file: C:\ProgramData\Tacsoft\Virtual Folder\Multiple Choice Express\QuizResources\Resources\Database
No, you can't print it on stationery, but you can preview it and the use Print Screen button on your keyboard to cut the area with the quiz to print it on a stationery.