You could separate the plants and have 2 instead of 1. The week growth and spare leaves are probably result of over-watering and lack of light. What kind of light is it getting? - is it in the window or more away from it? Using some supplemental lighting while indoors would help. Re-potting it into a better draining mix would help with drainage/water retention. Jades usually don't loose leaves because of re-pot, but because of wet conditions.

It may be good to get better mix and get the plant into more light so it gets healthier. There is no need to pinch jades weekly (probably not even for 'real' jade bonsai?)

Shortening branches may help to get bushier plant. And it will encourage more branching. Do you have idea how you like it to look? You could possibly cut off the branch on the right (and get another plant :) to get more tree-like plant instead of a bush-like plant - depends on what you like.

Looks like a Crosby's Compact.

I'd like to keep them together just because the roots have grown together and both plants are lopsided without each other. :)

It's getting south-facing sunlight but there are buildings across the street that are preventing it from getting more than 4 hours of sunlight each day. The soil I use is quite fast draining already; it's pretty much bone dry within a week and a half. I use lots of perlite and coarse sand.

I really like the look of this kind of tree: