Considering the Airspy v1/v2 and Airspy Mini are made by the author of SDR# it's pretty much guaranteed that yes both devices will work with SDR# - you can download the latest version of SDR# from the Airspy website:
Download | airspy.com
There is also a driver that can be used with both the Airspy and Airspy Mini
just in case the device doesn't work automagically with Windows the moment you plug it in. If it does work then you won't need to install that driver, so don't install it unless it's absolutely necessary.
And as long as a plugin is designed to work with SDR# and updated to work with the latest versions then yes, it'll work as expected which means the Frequency Manager Suite will work just fine as well.