How do I fix a stuck AC button on Honda Fit

You can try spraying some WD40 with straw around the edges of button so that the WD40 can penetrate into it and may unstick button.

how do I remove this button

It's relatively easy. It can be popped out from the front with a flat screw driver and pliers. Pry the button off first with a screw driver, then push the screw driver on the side of the switch body to release the side clip. I used a feeler gauge to hold the clip open but you might not have to do that. Use pliers to grab the button and hold it while you push the screw drive between the side clip and body on the other side. Once the button is loose, pull it forward and release the clip holding the wires. Don't worry about damaging the switch when removing it as it's already shot.