Do I have to chose in the menu
Mobilfunknetze → Mobilfunkanbieter: Available networks (only English?!)
a network manually or do I have to choose “automatically”?
Did it work before or are you trying to get online for the first time with this provider?
Sometimes a simple reboot helps with that sort of stuff.
Probably. I’m on Fairphone OpenOS, where dialing *#*#4636#*#* gives a test menu where you can fiddle around with some connectivity stuff. I don’t know whether it is there in Fairphone OS, too, but it’s a general Android thing, so there’s a chance … But don’t ask me what all those options there do in detail …
As long as you can connect to your provider just set (which is probably just choose) the correct APN for your provider which is pinternet.interkom.de according to your provided docs in the settings (german) Mehr -> Mobilfunknetze -> Zugangspunkte (APNs).
You are already connected to your operator’s network, because you can call and you see the triangle icon in the top bar showing signal strength, so you do not need to connect to any network in this menu. For internet, you need to check the other options in Mobilfunknetze, such as the APN.
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