The first issue doesn't appear to violate the EULA. You are not receiving the same functionality that Tableau Server provides by doing this you're simply streamlining what would have been a very laborious manual process of exporting static images (Not the same thing as publishing to Server).
Second issue does violate the EULA. Only one specific user is associated to a desktop license. Other people aren't allowed to use that license. 10 users, 10 licenses.......100 users, 100 licenses.
i see, thanks, thats why i was suspecting.
In the first case: if want to do this in a parametrized way( every friday to group x, every monday to group y) from a remote web application which calls this export script its allowed?,
In the second case, what happens if a employee is fired or is in his vacations, it means i have to purchase another licences to the new employee?
Yes what you described should be fine. In regards to the second question, you simply change the owner of a particular desktop license to the new owner within the customer portal @ https://customers.tableausoftware.com