Thanks for you details. Here are answers for your reference.
The answer for the first two questions is YES;
The signal transmission between the K3 and the controller is via RF; no gateway is required. If you want smart control, you can add a Zigbee 3.0 gateway.
One remote can work with countless controllers, one remote can be controlled by 12 remotes.
If there are any further questions, please feel free to contact.
Just one final clarification: can both FUT035Z+ controllers be paired directly with a standard Zigbee 3.0 coordinator running Zigbee2MQTT (Home Assistant), while simultaneously retaining their direct 2.4 GHz RF pairing with both K3-W wall panels?
I would like the wall panels to work independently of Home Assistant, while Home Assistant provides brightness and CCT control through Zigbee.