Does waving a magnet around create light? If I wave around a bar magnet, the magnetic field in the space around it changes. Is this enough to go through the whole speed of light derivation implying that the motion creates an electromagnetic wave? If so how do I determine the wavelength and direction of the resulting wave? 
 A: The proton is a very small magnet (both in size, and in magnetic field strength). Inside a 3 Tesla MRI machine, it will resonate (spin) at 128 MHz, and at that frequency it produces a radio wave which can be picked up and used to make images of the human anatomy. Well- usually you spin a bunch of protons coherently and measure the sum signal.
Problem is - as you scale up your magnet, it gets harder to spin it fast... So for a macroscopic magnet, you will emit only very low frequency E/M waves.
You asked "How do I determine the wavelength and direction?". The wavelength follows directly from the frequency, since all EM waves travel at $c$. So rotating a magnet at frequency $f$ implies a wavelength $\lambda = \frac{c}{f}$.
The direction is a little bit trickier - but if you are rotating your dipole about a particular axis, the radiation will follow a 3D "donut like" pattern, with no emission along the axis of rotation, and the strongest emission in a circularly symmetrical pattern in the plane perpendicular to the axis. See for example this presentation for calculations of a rotating (electrical) dipole - a lot of the math is similar in shape (although different in the details).
A: Technically, yes. The changes in magnetic and electrical fields will propagate outwards at the speed of light. The wavelength is determined by the frequency, so it would depend on how fast you were spinning the magnet. You would have to spin the magnet very, very fast to produce anything other than extremely low frequency radio waves. Even a 10khz signal would need the magnet to spin at 10,000 rps (rotations per second) which is 600,000 rpm. I don't know of any material that wouldn't rip itself apart at that speed.
A: You will get a continuous spectrum of electromagnetic waves, rather than a single wavelength. If you give the magnet a periodic motion with a frequency f, the radiation will have components at all multiples of f.
