Hi there, and welcome! This is a great resource, and hopefully you can find answers to all of your questions here.
I can get a couple of them:
1) Yes, leaving your hose hooked up is fine. You may want to get a pressure regulator to make sure you don't have surges inside the coach. they can be found at all RV stores. you also may want to shut the water off in case of leaks if you will be away from the coach for an extended period of time (you just never know with hoses).
2) Yes, the pump is for when you don't have pressure. It always helps to carry a good spare if you use your pump!
3) The water pump may be close to the tank - possibly under the bed. That's where it is in our motor home, but I can't say for your application for sure. Other folks will know that one.
4) Dunno about this one, sorry! We have a rocker switch in the bathroom, apparently for the water pump, but it seems to do nothing. I will have to look it up in our manual one of these days...
Good luck, and enjoy your great Airstream! We'd love to see pics if you have them!