First, if you purchase the AirPort Express from the Apple Store they have a return policy if you are not satisfied that it will meet all of your goals for it.
1. Can AX be setup as I have described above - to receive iPad playback (via wifi) using its own dedicated little network and output it via its audio socket to my PA?
Yes, this should work. Sorry, I don't have an iPad handy to verify it though.
2. Is there a better way to do this - something I have not thought of?
Again, what you propose should work. Of course, you should give it a try before attempting to take it on location just to be sure and to familiarize yourself with its operation.
3. I am concerned about performance of course. Music files playback isn't too onerous but if it's thrashing around with wifi will that cause any noticeable latency issues?
The latest (2nd generation) AirPort Express supports 802.11n wireless. So should be your iPad 2. This is more than enough bandwidth to handle audio streaming. Just be sure to keep the location of the iPad & the Express in the same area to prevent any unnecessary Wi-Fi interference to have a clean signal between them. Since you will be operating a Wi-Fi network, even though local, I would suggest that you use wireless encryption to prevent anyone from connecting and using up your network's bandwidth.
4. What might the impact be of using wifi like this on the battery? Currently a 2-our gig of playing music via an audio cable only uses about 15% which is excellent. Using wifi as well to transmit the signal will probably use more. I could of course plug into power but would rather use less cabling
The wireless drain would be similar to what you are getting now when your iPad is connected to the Internet via Wi-Fi. I would suspect that you will see a greater power draw on the battery and should expect that battery life will be affected ... but I don't think it would be significant ... unless you are already experiencing poor battery life. For example, if your iPad is several years old and is starting to have battery issues.