You can register and use the Gigaset E560 HX phones directly via DECT with your Fritzbox 7590. The Fritzbox supports DECT phones like the E560 HX, so you can easily use them as a replacement for your old C430 phones.

Yes, you can - but a small difference is important:

- The Gigaset E560HX is an HX handset (CAT-iq 2.0 standard). It is not operated via cable on the TEL connection, but is registered directly to the Fritz!Box 7590 via DECT radio.

Procedure: Activate DECT on the Fritzbox -> register handset -> deregister/delete old C430.
The TEL connection on the side of the Fritzbox is only intended for analogue telephones (with cable), not for HX handsets.

Are the C430 and E560HX models compatible with each other?

I have no network on my new phone...
If I disconnect my old devices completely, will my new phone work?

This means I want to deregister my old phones from the Fritzbox and only connect the new one to the Fritzbox at the side phone connection?