Yeah, supplemental light would probably help. Doesn't need to be a fancy grow light, just fluorescent (regular incandescent bulbs give off too much heat, will burn your plant if close enough to do any good) light shining on it from just a few inches away.
Mist is just to spray a fine mist of water on it from a squeeze spray bottle.
Humidity tray is a shallow tray a bit wider and longer than your pot, with gravel/ small rocks in it. Fill the tray with water and then set the pot on top of the rocks, so that it is right over the water, but not touching it.
Note that imafan is in Hawaii, thus the idea that Carmona could become a weed. Not anywhere that has freezing winters.
You don't want to fertilize trees that are already stressed, so I would withhold fertilizer from yours until it starts putting out new leaves.
Carmonas are noted as being sensitive trees, not always easy for beginners. But very beautiful when flowering. Good luck with yours!!