connectors are usually different on differnet motors depending on where you buy them from. Sometimes they dont' even have any, so you just install your own. Often enough motors don't come laced in a wheel (or are badly built wheels that have to be at least tensioned and trued, and too-often replaced entirely after they break), so you may have to build a wheel anyway, even with a new motor.
CA v3 is not a controller; it's just a "computer" that controls your controller.
It's probably a lot simpler to have your old motor relaced to a new wheel, if you're already moving everything over to a new bike, than to go thru all the things you'll need to do to setup the bike with a new motor. That's just a rim and set of spokes, which any *good* bike shop should be able to do for you easily, and if they won't, it's actually easy to do yourself if you are willing to try. There are a number of threads around ES on lacing / building wheels, as well as good sources for spokes and rims.
