Read sim data in airplane mode If I activate airplane mode, then put a sim card in my cellphone. Can system apps and other apps read data from my sim card, like phone number or network provider?
Yes. 

Aeroplane mode is to only deny access to network. System apps  can access SIM information when in aeroplane mode. So can installed apps, if they are granted permissions to access SIM. For instance, install this app SIM card contacts , put your phone in Aeroplane mode, grant  permissions to this app and you can transfer information from SIM to phone and vice versa