What would happen if we cut the corpus callosum? How would a two-halved brain work? If it would, could we still control things like motion, and would hearing, vision, and other senses still function?
Basically the same as a normal two-halved brain. Circumstances in which function is altered are fairly limited. For details, see case reports on Wikipedia's split-brain page, and this episode of Scientific American Frontiers that features Mike Gazzaniga's research, as mentioned here. Gazzaniga's research was reviewed in a Nature news feature (Wolman, 2012), which you may also find helpful.

Also, yes to all questions of control, except maybe hearing...not sure how we control that normally, other than in terms of attention (see "Do we only hear what we want to hear?"), which still operates normally AFAIK. Control breaks down unusually in mostly special circumstances where stimuli are presented to only one side of the brain. Both ears usually hear most sounds, and both eyes' fields of vision overlap quite a lot, so these circumstances need to be created experimentally to demonstrate really clear effects.