The issue right now is that when I in 'Næste gang?' selects an option, fx. 'Daily' or 'Weekly', the Record will update and get a new deadline based on my choise (daily or weekly). However the Record also looses all it's data, fx. Assignee and the 'How often' all the way to the right (let me show you):
How do I change this, so that the Record will appear in the right Group when updated?
Hmm, I'm having trouble understanding your table. From what I can tell, you have four fields with data: Task, Date, Yes/No, Frequency/How Often. I'm not sure what "Næste gang?" is, since what you describe sounds like a dropdown that interacts with a script or automation. My best guess based on the information provided is that your script/automation creates a new record and copies the record name, but not the other data associated with the record – if so, then the solution is to edit the script/automation to include the data.
So 'Næste gang?' would be "When should the deadline for this task be next time?" -> the user can then choose between 'A week', '1 day' or '3 days'.
Then the field 'Næste deadline' (Next deadline) looks at the choice of the above and automatically adds the next date. Is it in this formula I should add the data for the rest of the Record, fx. Assignee?