Get rid of the mostly peat soil, get some small size aquarium gravel, some perlite, and a little good compost. Mix it all together (compost no more than 20% of the mix if that, for very fast drainage, and perlite 30-35%) and plant it in there. It may seem weird if you're not used to it, but it's the way to go for your tree. Give it the absolute most light all day long that you can and water only every 3-4 wks in winter. Don't let the pot sit in the drain water whatever you do.

You can certainly continue to use your potting medium, but you may want to add some extra perlite to it to increase the porosity. Most peat-based mixes tend to be mucky.

Though we can't tell without seeing it, I suspect that you could keep it in that two inch pot for a while, yet. They like to be somewhat cozy.

Your watering frequency will depend upon several things: the size of the container and the plant, the kind of container (clay or otherwise), the temperature and humidity of the room, amount of light, etc. These are plants that should be considered succulents, as they store a lot of water in their stems. So, after a good drenching, you should allow it to really dry out....and then some.