Hvad kan jeg hjælpe dem med, frøken?
The capitalisation of dem is the important part here. Since you also seem to learn German, it's just the same there: de/deres/dem (Da) and sie/ihr/ihnen (Ge) for they/their/them, and De/Deres/Dem (Da) and Sie/Ihr/Ihnen (Ge) for the formal you/your/you.
Ah, not exactly. These sentences have slightly different meanings, in both English and Danish. They are not different levels of politeness.
- What can I help you with? - Hvad kan jeg hjælpe Dem med? = Is there something within my skillset that I can do for you?
- What may I help you with? - Hvad må jeg hjælpe Dem med? = Is there something you allow me to do for you?
That's usually what English teachers tease you with if you say "Can I go to the bathroom?" or something. "Can" denotes the (physical or otherwise) ability to do something, "may" asks for a permission.