If you enter your email address in the Contacts app, it will give you auto-complete suggestions as you type. You can start typing either the email address or your name to get the suggestions.
You can also start an email directly from the Contacts app by tapping on the email address.
Sorry, but there is no way to prevent the App Store from closing while your app downloads (or while updates load, either). It's just the way the iPad works with the App Store (unless, of course, you have a jailbroken iPad1, then you can add a tweak to prevent this behavior).