Can it connect to an Xbox

The product is compatible with Switch/Switch 2 and Windows, but there is no mention of compatibility with Xbox.

How does the integrated charging dock function with the 8BitDo Ultimate 2 controller?

The integrated charging dock keeps the controller always charged and ready to play, automatically reconnecting when removed from the dock.

The TMR joysticks provide higher sensitivity, greater precision, and enhanced durability while consuming less power.

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8BitDo Ultimate 2 Bluetooth Wireless Controller with Hall Effect Triggers, TMR Joysticks and Integrated Charging Dock - White - 81HE01

Customizable 6-Axis Motion Control - Enjoy enhanced motion-based actions with 6-axis motion control. Customizable in 8BitDo Ultimate Software.
Integrated Charging Dock - A seamlessly integrated charging dock keeps your controller always charged and ready to play. Automatically reconnects when removed from the dock.
Hall Effect Triggers & Mode Switching - Easily switch between linear Hall Effect triggers and non-linear tactile triggers for optimal control across different gaming scenarios.
Equipped with TMR Joysticks - The first 8BitDo controller to feature market-leading TMR joysticks, offering higher sensitivity, greater precision, and enhanced durabilityall while consuming less power.