You can undelete mail by simply moving it back from Trash to your InBox.
Some apps - for example Apple's Pages - has an undo function, but it's on an app-by-app basis, there is no global undo provided for all apps by the iPad's operating system. So, if an app offers 'undo' then it's available, if the app developer chose not to offer it, then it's not available.
I wasn't sure about your other questions, so I'm sure another Member will come along with some more answers...
Tim