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You should be able to insert the date into a file name using powershell or whatever else you're writing in. There is this link: Append Today's date to file name (batch file) that's specific for tableau but the whole file name part will be separate from the tableau side of programming. You should be able to look at stack exchange or any other techy area to get a a better script than what I could write quickly for you.
Is there any method for raising an alert if the data in the tableau server goes empty?
There is, but i haven't personally investigated it - I believe that although its made by a Tableau employee (Matt Coles), its an extension rather than a supported product.
For further help, you would be better getting involved in the Viz Alerts 'space' of the forum