Figured I'd update this a bit.
Anyways, I've been doing as you guys said: Lots of sunlight, watering when needed only. Wondering what your opinions are on the state of the tree and what I could do.
Many issues at the same time, Valtiel.
The white stuff is calcium deposits from your tap water. See the edges of the pot? Full of hard whitish calcium?
Yes, rain water is the best.
Then, the stones; they are cool, but they are not allowing the water to go down to all your rootball.
Same here with the suckers and the weeds; they look nice (and see how happy they are? They are not dying...) because they are taking all the nutrients in the soil and leaving nothing for the roots of your bonsai.
So, IF the tree was mine, I would take the pebbles off, the suckers off, and would try to get a better quality water to water the plant (which is difficult if you live in a flat).
Carmonas are NOT the easiest trees to keep happy indoors, so don't feel too bad about it.