Do I also have to apply for fields without restrictive admissions?
No. As a German citizen or academic national (international applicants with a German “Abitur") you are allowed to register for entrance-free subjects (even without a prior application) at least one week before the semester begins.
Necessary information and documents about matriculation
Note: EU citizens, citizens from EEA member states (Iceland, Liechtenstein, Norway) and other international applicants without a German “Abitur” must apply for entrance-free degree programs at least one week prior to the start of the semester.