Yes, the AC plugs directly into the controller and basically acts like an on and off switch for the AC. It plugs into the socket on the front of the controller. You can see the socket in my first picture (I just unplugged the AC so you could see it).
To bypass the ACs thermostat, the AC is set always on the "on" position and on the coldest temperature on the AC, that way it never turns off on its own. The controller turns it on when it senses it's too hot and once it reaches your set temp on the controller it'll turn it back off again.
As for the drainage, I have a drain at the bottom in a corner. The tank isn't level so that it'll drain towards this corner. Right now the plants are just sitting on the floor but I think I might raise them up off the ground in the future.
If you and your dad ever want to come over to check it out and see it in person, you're more than welcome to. Sometimes seeing it in person makes a big difference