Tell us about yourself!
If you use glow in the dark paint (contains Zinc Sulphide) on the surface you want to project onto then you will get enough persistance to form an image. I have been thinking of using a rotating mirror on an old VCR head to produce the vertical component of a raster (it would be easy to sync to a video), a much faster motor will be required for the line frequency though. Good luck with generating some raster images. The code to draw a raster will be fairly simple, increment x until it reaches max, then make x = 0 and increment y, when y = max reset all to zero, increment your counter, repeat. Modulating your image from a file while where [ x,y]counter = laser on or off. I hope this was helpfull.
You need quite a lot of current to make the wire hot, something like a phone charger would have its internal thermal fuse popped in no time. Batteries can provide the current, they will get hot themselves and that could be an issue. The idea of a transformer is good, I remember my father using one but it was quite large, maybe a few pound in weight!