UE5 support will be added soon for Python3.x asyncio support.

Primary buttons work with armature's bones only. Make sure you're using proper namespace for your character and buttons are linked with armature bones properly. If that doesn't work, contact the support.

Official Maya support will be added soon for Python3.x asyncio.

X-Pose Picker is really easy to integrate with any software using TCP protocol. The easiest case is when application provides Python3.x scripting. With that integrating X-Pose Picker with the software is  almost a no-deal and can be done by anyone who knows basics of python scripting by modifying existing Blender server template.

Possibly yes, however there's no server plugin available for the Unity yet.

Theoretically yes, however add-on may run into some stability issues. Older version of the add-on still may work however new picker releases will no longer support Blender 2.7.

Yes, in 100%. Just use the linked character's proxy armature name as the namespace for the picker.