You can click on the bed in your room to take a nap, which skips one periode of the day. Reversing time is not possible I believe.
As far as I know there is no infinite money code or anything.
Can't help you with the store
Did you find all the culprits? There should be three students involved. I'd recommend talking to all the students and teachers to get the dialogue option
Bit of a spoiler but you need to find the thief of the blueprints in the sisters club. Basically follow the club story line
Where can I find a character named Archie. The engineer told me to talk to him but I can't seem to find him.