Yes, this is possible. (Tested with "old" telephone purchased from Swisscom and successfully coupled with the new Sunrise Internet Box).

The following instructions were found on the phone for the manual connection:

"You can connect the HD-Phone manually to the Internet Box / base station.
Select > Menu > Settings > Advanced. Settings > Login > OK, then press the + button on the Internet Box".

Instead of pressing the +button, the DECT button had to be pressed for more than 2 seconds on the Sunrise box in order to enter coupling mode. There is certainly a similar procedure with other providers.

No, the telephone only works with a Swisscom Internet box. It can therefore not be operated with other routers such as UPC.

Unfortunately I do not know that either