Hey SirCryloc - welcome to the Ubisoft Forums!
All of your Ubisoft Store purchases are permanently associated with the Ubisoft Account used. In terms of PC games, they are added to your Uplay library and remain there for you to access.
You would not be charged again to install the game on another device, as you have already purchased it.
Hey there phase.verocity!
You should be able to download Ubisoft Connect, and any games within the library, on two different computers at once. You may not be able to launch them both simultaneously and play the game on both computers at the same time, though. You will only be able to play any games on one computer at a time.