Certainly looks like a Jade Plant (Crassula ovata)
I'm not the best at taking care of the things, despite having a certain fondness for them (the college greenhouse I'd visit to get out of the winter blahs had a specimen in a not terribly large pot (25l, perhaps) with two trunks about the size of a human thigh.)
Mine seem more prone to drooping (like your rightmost trunk) than to maintaining that nice upright tree-like growth. Perhaps I need to prune more. As for training, the wikipedia entry claims that they are a good/common first Bonsai project.
The yellowing may be from too much light - a shadier spot might suit it better.