some part of your question was explained in this post:
The Listener would be ideally in UWB range with the Tags.
The Gateway would be ideally in UWB range with the Tags and Anchors.
There is nothing like “minimum anchors the listener must see at the given moment”. I think you have misunderstood the concept of the Listener. Please see the post above.
No. The position is calculated on the Tag and its position is collected directly by the Listener or Gateway. The Listener was intended to be used only for demo purpose. The Gateway in contrary provides more complete functionalities like uplink/downlink of Anchor/Tag configuration and IoT User Data.