Jbing does not void the warranty unless you get your device to a state where you cannot restore it. So long as you can restore your device back to original your hardware warranty should not be affected.I think so. There is a way to convert your iPhone to an "AirServer" which can receive an Airplay signal over the local wireless network from your MBA. The signal is routed through the network to the phone which is connected via a cable to the TV.
You will need a jailbroken iPhone and some software from Cydia. Search google and you should be able to find what you need. I'm probably going to do this soon but I haven't had the time recently.
Edit: I should add, you will void your warranty by JBing and you should make sure it's not illegal wherever you are - I don't think it's illegal in the US anymore. Also, I don't think the software that you require is commercial so you shouldn't run into any piracy issues.
aren't those cables huge dollar anyway? Wouldn't you be better off in the long run to save up a bit and buy an Apple TV?I have an iPhone 4s that I plan to connect to my tv with an apple vga connector. Is there a way to use airplay without an apple tv to stream movies from my 2011 MBA?