Is there a possiblity to set the required user level to move a category to another category? Or is it simply possible to disable the possiblity to move a topic besides you are a admin / moderator?
Not really. Maybe read about trust levels in Discourse. Trust Level 3 is able to recategorize topics.
1 me gusta
Thank @MarcP. I know that TL>=3 is able to recategorize but, this is not what I want. TL4 would be OK or disable the re-categorize feature completely.
You can not do this at this moment.
Then, this is a feature request 
Or, I will work on this at the weekend.
You can change the settings to reach the Trust Level 3 so that nobody can reach it. Without the TL3 nobody will be able to recategorize the topics except the staff. Then you can assign the TL4 to the users you want to allow to move the topics between the categories.
3 Me gusta
Yes, this can be done by disabling the trusted users can edit others site setting. See What does the “trusted users can edit others” setting do? for details about the setting.
2 Me gusta
Pequeña actualización sobre esto: ahora tenemos un par de configuraciones separadas que se pueden habilitar en grupo para dar más control sobre esto. 
edit all topics groups permite que los grupos añadidos puedan renombrar, etiquetar y recategorizar temas. Así que cambiar eso solo a, por ejemplo, administradores, te permitiría restringir eso a los TL3. 
Y edit all posts groups cubre los grupos que tienen la capacidad de editar publicaciones globalmente (por defecto, TL4 sigue siendo el mismo).
1 me gusta