1) You can use Apple Configurator to manage them but you need a Mac Book or you can use Meraki MDM which is free or you can use both.
2) You cant lock the home screen but you can refresh the device using the Mac Book which will restore it to the state you originally set it to no matter what the kids do it. This is a common problem in schools.
3) You cant stop them setting locks but you can hide the settings in folder some where and set restrictions, but refresh of the device will resolve the problem.
4) You cant stop them from turning off the wireless.
5) The good thing if the kids do anything, you can refresh the device and it go back to its original state you set it up to using Apple Configurator.
6) Updating the Apps. You can use Apple Configurator to update the Apps which takes a while per case or use Meraki MDM which does it over the wireless, you can push.
7) Flash does not work on the ipads. Workarounds some companies tell you to use Puffin Academy, it works sometimes and sometimes its slow or has problem loading. I think its due to the Puffin Browser using their own proxies which at sometimes of the day can get overloaded.