Question about Panasonic Rp-Tca430e-S

Yes, if the handset has the 2.5 mm jack socket. However, I don't know whether Panasonic is the best match for Gigaset in terms of listening quality.

Oops, no idea. And above all, I never bought this thing. LG Fortunat

Panasonic RP-TCA430E-S
"The special headset enables hands-free telephoning so that various tasks can be carried out on the side. The device is connected to the handset's 2.5 mm jack socket."
CL660HX
"Interfaces
Connection type headset 2.5 mm jack
Micro-USB 2.0 interfaces"

So yes.

Yes, if it has a 2.5 mm jack socket