1. I would use either a switcher/scaler to send two signals if you are displaying live video with cameras and also are sending a signal from the computer.
2. If you have a camera AV mixer it should be easy to send a signal ,with the proper equipment, over from the computer to the mixer. You can run the hammer about 60 to 75% with the words being more prominent.
3. If you are using stock video and are looking for a seamless program to run video over lyrics I would recommend a program called liveworship,
http://www.liveworship.com right now I am using it on a MAC and it works great but it can also be used on a PC also something that no program, I am aware of, has the capability of doing. The video over lyrics right now is a bit choppy but I have talked to the developers and they are working on a solution.
To better help you I would have to know the layout of your system. Please post what you have and I can better figure out the best solution for you.
