Zeki searches for the money underground using GPS on his phone. However, GPS doesn't work underground.
Zeki is looking for a job as a caretaker at the school. After he faked an alarm, he's getting the job interview with the school's headmaster. This is not possible in Germany because school caretakers are hired by the local authorities. Headmasters are working as a public servant for the federal state; they have no influence on hiring a man working for the local authority.
Lisi finds out that Zeki faked his diploma and that he is not a real teacher by searching his personnel file in the headmasters office. In Germany, the personnel files of teachers are not stored in the schools but at the ministry of education.
Attacking a pupil like "teacher" Mueller did in the pool would lead to serious investigations and eventually sentence him in a disciplinary enquiry. On the other hand it wouldn't be possible to attack a teacher like the pupil did before without getting into serious difficulties with school authorities. This is in no way possible in German schools without consequences - and in fact it's an extremely rare behaviour at German schools (which doesn't mean that it is not possible - but when you act like shown, you would be in serious trouble, both pupil and teacher).
When Zeki and Charlie are talking on the phone, the display of Charlie's phone shows a number pad. However, this is only displayed before you make a call, specifically to dial a number manually. During a call, when the phone is next to an ear, the proximity sensor would turn the screen off.
There is no meaningful reason or explanation why Charlie is at the school at the time when Laura finds Zeki's note in her locker and brings it to Lisi.