Will find my ipad work if the ipad is turned off? Will all apps on an ipad appear on the main screen, or can they be hidden?

You can not find your device if it does not have an internet connection; so if it is off or out of communications for some other reason then Find my iPad will not work. You can tell it to notify you if the iPad is turned back on and connects to the internet.

In general, apps can not be hidden. Some few apps, like Safari and the App Store can be turned off in Settings > General > Restrictions. When they are off they will not appear on the home screen. If you do this do not forget the passcode you set. Recovery from forgotten passwords is every bit as difficult as it should be.

Otherwise, the best you can do is place the unwanted apps in a folder and move them to the last Home Screen, where they will be less obtrusive.

As long as the device is in range of a wifi network it has previously connected to AND you have push notifications enabled it will check for new push notifications every so often and it will update it's location at that time if Find my IPad is enabled.

If it's a 3G Model as long as it can get on wifi or 3G data it'll work.

This assumes you mean asleep, and not actually powered off by pressing g sleep until the slider appears and turns it off that way