Well, taking air out of your room is called an exhaust and bringing it in is called an intake. In my room with 2K right now I just have a Dayton blower as an intake bringing in cool air in from out side and it is working fine, will need to change things around in the summer, but for now it is fine.
Well as far as your light, you can run a heavy duty extension cord to a plug in that is not on the same breaker as your bathroom plugs and you should be fine, for instance, try running a plug from the living room or a hall way plug. Just make sure that the extension cord you get is rated for about 1300W and I would plug it into a power strip because if the light starts to pull to much electric then the power strip will just trip the on and off button and you don't have to get into your breaker box and mess with anything.
Hope this helps.