A:AnswerYes as long as your PC has Bluetooth, plug in directly via USB, or you have the XBox wireless adapter for PC. In my experience, some games such as Watchdogs Legion did not seem to like Bluetooth but worked just fine if plugged directly into USB or using the wireless adapter. Control worked fine over Bluetooth though so just something to be aware of if you hit issues with blutooth like I did.
A:AnswerYou can remap the controls in the xbox accessories app that you can download from the microsoft store, but the share button doesn't do anything (at least that I'm aware of). Also you have to update the controller using the app in order to use it wirelessly.