Looks healthy to me. Maybe just trim it back so it grows taller and thicker. You can transplant the cuttings (even placing leaves on soil will stimulate them to grow).

I think it is quite etiolated - long and contorted stems that have been turning toward any available light. I believe I see at least couple of dry/dead stems too? I don't think that is serious problem, maybe it wasn't watered enough.

Plant's leaves look good otherwise. White dots are most likely some salt/minerals deposits from water that can be wiped off easily - not much problem there. Oldest leaves often yellow up, dry up and fall off. But yellowing could be caused by overwatering too - in that case, they feel soft, full of water and almost translucent yellowish color. That means soil is not draining well and the roots are sitting in wet muck. That would be problem for most plants. I can't tell from the photo. If there are many leaves yellowing at more-or-less same time, I would consider checking the roots.

I would cut off all dead branches (they will fall off anyway). Decide how you want plant to look. Some prefer droopy branches - I prefer more compact growth with thicker trunks. Depending how you want plant to look, it should be pruned.

It definitely should be given much more light than it had before. If light happens to come from mostly one direction, turn it 1/4 turn every week or two to expose all sides as equally as possible.

I would amend the 'soil' you used by adding lots of sifted or rinsed perlite, It seems to be water retaining - succulents should have very good drainage. You can check if the potting mix is dry or still wet before you water. Use bamboo skewer or chopstick. Insert deep into the pot trying to avoid roots. Take it out after few minutes. If dry and clean - time to water. If damp - cold and has even some particles sticking to it, make sure you don't water. Check again in few days.

Edited to add: air roots are not much of problem; sometimes they may grow if there is plenty of humidity. It is suggested that they may grow if plant is thirsty - but rather check the soil for that. Air roots could be rubbed off, eventually they will dry up. If you take cutting and it has air roots, they will most likely continue growing. But jade cuttings root very easily, so you don't have to worry about having air roots on them.