Assuming someone lost an arm, is it possible to do the equivalent of cloning a new arm and attaching it without losing essence? You aren't gaining any kind of special advantage, barring not missing a limb anymore.

Yes and No. Cloned replacements are the norm. If you can't afford one, you can get one that an unscrupulous guy chopped off of a compatible homeless person, though a second-hand limb wouldn't match the rest of your body.

Yes. See Augmentation. (sorry that's it).