There is pretty much you can do. Check section for
Extending the CSS file...
Does this change the class on all UL lists that are created in the WYSIWYG - I would like the user to highlight their list and pick a style from the Style Drop Down (Apologies - I wasnt very clear in my initial post)
It's possible to just mark the element you wish to style and then select from the dropdown for the style yes
ChangeElementType. Lets you apply a class and change the element type for text block elements (p, h1, h2, and so on)
Is it possible to customise the TinyMCE WYSIWYG control so you can style the Bulletpoint lists and links, for example add a class to the UL:
And also style links:
I hope this makes sense,