What ports does it use? Do I need to open anything on my router?

Cloudless File Transfer uses:

• UDP port 41234 for peer discovery (broadcast)
• TCP ports 41235-41245 for file transfers (it starts at 41235 and picks the next available port if that one is in use)

You do not need to open anything on your router. All traffic stays on your local network and never leaves it. The only firewall that matters is Windows Firewall on each machine -- use Settings > Add Firewall Rule to configure it automatically.