On a Use Case diagram can you show things that an actor cannot do, for example because they won't have permissions to do it?
Or is it just implied due to the fact that they won't have a line joining them to the particular use case?
If the Use Case you are diagramming is the case where an actor attempts to do something that is not permitted and is then denied, then yes, I would show it.
Otherwise, I would stick to only including things that are actually part of the use case.
No. An Actor would be connected to everything that he can do. If the Actor can't do it, then it's not shown.
This is what alternate paths are for. The basic path (a.k.a. happy path) will show what happens when the correct Actor initiates the Use Case. In the alternate paths you can show what happens if the wrong Actor attempts to initiate it.
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