The registration can take (unfortunately) up to 3 months. During that time, you can only move around the area, where you have been registered = the city, town, county.
When you receive your 'ID', a green card with your photo, name and the address of your actual location inside, usually written in German, it says how long it is valid and on the back it tells if you have any restrictions in moving. Once you get this ID, please make sure you check this information.
In any case, German bureaucracy is extremely strict, there is no way to make it work faster. They have to deal with hundreds and hundreds of applications each day and it takes ages to make the things right, but in the end it is effective and it works.
And always always feel free to ask the people around you.
If you want to report any case of abuse, you can have a look on this websites, this organizations can help you to get legal advice about these situations and make sure your voice is heard.
(free legal advice for social causes)
(records from refugees experiences)