Do you know if I can use Visio to forward-engineer a sequence diagram into code (c#)?
Can it be done with Visio alone or do I need a plugin?
What about other diagrams?
You have to get the Visio that for users of Visual Studio. See this link: Visio for Enterprise Architects for more details. The code generation capabilities are fairly weak and you might end up getting Visio into an inconsistent state. I know that Visio will let you forward and reverse engineer both code and databases, but both capabilities are very limited and I don't recommend doing it.
In my opinion, Visio is a diagramming tool and it should be treated as such.