3 mice in and nothing works

First, most major brand mice should work fine, so avoid the direct from China products on Amazon as many take hardware and firmware shortcuts that prevent them from connecting to anything but a PC. Your Bluetooth mouse would only work if it has a wireless dongle that connects via USB, and if it is a non-gaming mouse it may have a slow operating speed (less than 1KHZ) which would cause a very slight but usually unnoticeable delay. It is entirely possible that your settings caused the sensation of input lag, rather than actual input latency. Please read this and test your mouse again with it set to the highest DPI settings and match the K2 App DPI setting to it. Set the mouse sensitivity in the K2 App to something low, like 25 and start moving up.