Haupauge(i actually have some other brand) manufactures TV transceiver/receiver kit. It works in 2.4GHz band. You need additional battery pack transeiver(camera)side, some RCA2RCA cables. Very easy to use. But it doesn't work more than 15m if You have walls in between.
Wireless video is a tricky one. You can get units that work on 2.4GHz for fairly cheap (less than $300) or you UHF that are quite expensive (about $3000). My experience with them is that they don't work very well. But I've only used the $500 or less versions. At NAB this year though I did see a very interesting product that transmitted the video over Wi-Fi. I talked to a Steadicam operator that I know who was demoing the thing, and he said that it worked very well. It was called Cam-Wave, and it costs about $3000. The only other choice that I know works based on other opperators is the Modulus 3000 system, again about $3000. So in short, you get what you pay for.
Wireless video is pretty hard to keep "constant". Last September, I worked with ESPN on their reality show, "Knight School". They all used the new sony XDCams, with wireless video transmitters (UHF). They were pretty decent, and worked in far disntance. But anytime there was a lot of movement around, the picture would get distored w/ a lot of noise and static.
If you plan on keeping the camera stationary, and not too far away from the projector, then you should be set.
And yes, you can record at the same time you are transmitting.
The cheap wireless systems suck, not worth it.
That WiFi system mentioned above is made by wevi (www.wevi.tv) It's your best bet for price and quality, but there will be a LAG of about ½ a seccond, which will be a major issue if the screen is in the same space as the camera.
Best choise, if possible, use a cable, even if it means some extra work.