The 4-finger swipe upward is the same as hitting the home buttons twice to reveal your multi-task bar.i am assuming that you are on the most current version 5.1.1.
I am not certain why your email is not creating that swoosh sound when you send emails off. You've done all the immediate fixes, you have gone to your iPad settings and checked for your side switch that it isn't muted, checked notifications, checked volume cranked up high enough....not sure what else to say.
May gave to follow up and make an appointment a genius at the Apple store. Sorry, I wish I could be of more help to you. Maybe others could chime in.