The 'fuzzy growths' are normal protective bud coverings the plant will slough off if buds emerge. You'd have to disclose more details if you want to figure out the disappearing leaves, but if it's not the prime suspect (over-watering) this plant is a magnet for scale & mites, so those are the first three bases you should think about covering.

Al

My mom has been watering it; she says she has been watering it heavily once a week. That shouldn't be enough to cause over-watering, should it?
The fukien tea has been next to my healthy fig for the past several months; I read that scale insects love figs, so even if I somehow missed a scale when looking the fukien tea over, I'd imagine my fig would be showing signs of sickness. I think scale can be ruled out, thankfully.
As for mites, there was a spiderweb underneath that lower horizontal section of the trunk. Or rather, I *thought* it was a spiderweb, but now I'm not so sure. Some of the dead leaves were hanging from the branches by some sort of very thin string-like material (at the time, I assumed it was cat hair or some other thing that shouldn't cause worry) that could've easily been single strands of a web. I did destroy the web. I'll keep a close eye out for any more webs and the mites themselves. Is there anything you can recommend me doing if this is mites?

Scale is the most prevalent pest on this plant, and usually very difficult to spot - so be sure you did check very carefully.

Mites can be controlled with regular (weekly) misting, using a 50/50 mix of water and rubbing alcohol. Better though, is a mix made with water, rubbing alcohol, insecticidal soap (Castile liquid soap or Murphy's Oil Soap can be substituted), and cold-pressed neem oil. Ask if you want the recipe - it's effective against a LOT of pests.

Al

I did another check for scale. Happily, I still didn't see any signs of them. :) I'll continue to keep an eye out for them.

Could I have the recipe? It sounds very useful!

Spritz all plant surfaces, making sure coverage is complete, especially in leaf axils & undersides of leaves. Shake while using so oil stays emulsified. Don't spray in bright sun. Use all the mixture same day or discard. I've never had a phytotoxic reaction to this mixture, but if in doubt, test spray a portion of the plant & wait a few days before treating the whole plant. Repeat at 2 week intervals until the problem is under control.

Neem oil doesn't have an impressive knockdown, but the alcohol does. Neem works partially because it's a powerful antifeedant, but mostly by preventing insects from completing their life cycle.

Al