Well, I tried to set it up ob my parents iPad and it demanded that they also own a smartphone with the same phonenumber.

They owned feature phones so they've been blocked. Telegram paired just fine and works on any number of devices without linking them together and worrying about connectivity/battery for the main device.

Yes. It uses the phone number as the user identifier, and the non-phone versions assume that you have a phone that you're using as the primary device, and any other devices are secondary. The primary device is mostly because tablets and desktops don't have a phone number to use as an identifier. The battery/connectivity status of that device doesn't matter a whit after the secondary devices are setup.

So you must have a spyPhone tracking you. Perfect security...