Welcome to the party!
1. The tuner is toggled on/off when a CC value of 64 or greater is sent to the H9. It sounds like your controller is sending 0 for one press, and 127 for the next press, that’s why it is taking 2 presses to toggle the state (a CC value of 0 won’t do anything). You should configure your controller to always send a value of 64 or greater and then it should only take 1 press to toggle the tuner.
2. Sorry but I cannot reproduce this issue. I am able to map a CC to Middle Footswitch and Tap Tempo, and they both seem to work correctly. If you provide some more information about your setup that may help.