Dear @T4om
Thanks for the update.
Could you please share the case you bought (the links and pictures)? Preferably in the case dedicated thread - Fairphone 5 Protective Case - needed/Alternatives?
For one, I am definitely looking for something like that.
On restricting mobile data, please check the SIM settings, under the heading - using data by applications. There you can at least restrict background mobile data I think.