Yes, the Gigaset Premium 100HX device has a call blocking function. You can block certain numbers or configure call restrictions. To do this, navigate to the Settings menu, select the "Call Blocking" or "Call Restrictions" option and add the numbers to be blocked or configure the call restrictions according to certain criteria.
I don't know if I have understood your question correctly. Unfortunately, this product is NOT a base station, but only an (additional) handset. I didn't read everything correctly when I placed my order and was accordingly surprised. I actually wanted a base station. To make calls, you need either a compatible DECT base (doesn't have to be from Gigaset, just something compatible) or a router with DECT function (e.g. Fritzbox with corresponding function). In the end, I paired the handset with my Fritzbox 7583. It works without any problems.