The first gen iPad only supports up to iOS 5.1.1, if your tagline is correct and it's on iOS 5.1.1 then it's on the highest version that it supports.
You won't be able to install apps which require iOS 6+, though you may be able to download an older compatible version of the app : the app will need to be in your account's purchase history (so you will need to download the current version on your computer's iTunes to get it there) and you might then be able to download an older version via the Purchased tab in the App Store app : Install the latest compatible version of an app on an earlier version of iOS or OS X - Apple Support (if the app is paid for then check with the developer first to see if they support the downloading of previous versions, not all do)
For FaceTime no, the first gen iPad doesn't have cameras and therefore doesn't support FaceTime.
You can add an email account to the Mail app via Settings > Mail, Contacts, Calendars > Add Account. Or do you mean something else by 'set up my email address' ?
If you don't have access to wifi network then you could use an iPhone as a personal hotspot (if your phone carrier supports the function) for the iPad, or you could get a mifi device and use that as a mobile hotspot.
You don't need any app to help it run smoothly, iOS does that (and iOS is a sandboxed environment, each app controls its own data, other apps can't access another app's content)