Yes, in 100%. Just use the linked character's proxy armature name as the namespace for the picker.
Theoretically yes, however add-on may run into some stability issues. Contact the support which will provide the "working" add-on version for older version of the add-on.
Possibly yes, however there's no server plugin available for the Unity yet.
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.
Official Maya support will be added as soon as Maya gets official Python3.x asyncio support. For now it's possible to write own plugin based on TCP communication for Python 2.x.
Primary buttons work with armature's bones only. Make sure you're using proper namespace for your character. If you're sure all is correct try to change the port setting to different than 5555 for the picker and your host program. Start from increasing this number by one to 5556. If that doesn't work, contact the support.
UE4 support will be added as soon as UE4 gets official Python3.x asyncio support. For now it's possible to write own plugin based on TCP communication C++.