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.
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.
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.
これに関する小さなアップデートです。より詳細な制御を可能にするために、グループで有効化できるいくつかの個別の設定が追加されました。 ![]()
edit all topics groups は、追加されたグループがトピックのタイトル変更、タグ付け、カテゴリ変更を行えるようにします。したがって、これを例えば管理者のみに変更すると、TL3 からそれを制限できます。 ![]()
そして edit all posts groups は、グローバルな投稿編集能力を持つグループ(デフォルトは引き続きTL4)を対象としています。