It sure does! RetopoFlow v3 works in Blender 2.8x and up.
Both v2 and v3 are included with your purchase. Blender 2.7x users must use v2.
When running the 3.x.x version of Retopoflow on 2.8, you'll find it quite different from the 2.7x version. The Retopoflow button to start the suite can be found in Object/Edit Modes, and placed next to the Object menu button.
From Object Mode:
Click the Retopoflow button and choose the RF: Create new Target menu item.
From Edit Mode:
Click the Retopoflow button, and choose the menu item of the Tool you want to use.
You sure do! v2.0 and v3.0 are both free upgrades for all prior customers.
RetopoFlow uses the Add-on Updater module to allow updating from right within Blender!
If you have version 1.3.0+ installed then simply go to the User Preferences > Add-ons > RetopoFlow and click Check now for RetopoFlow update, then Update Now.
Alternatively you can update by first removing previous versions of RetopoFlow and then installing the new version via User Preferences > Add-ons > Install from File. From the file window then choose the downloaded .zip to install.
Yes! RetopoFlow works on any system which Blender supports, including Mac OS, Linux, and Windows.