How can I tell what the font size of the currently selected type is?
It depends: if the selected text has a size attribute, you can look at GetAsCSS() or GetAsSVG() to get it. If it doesn't (and for most purposes it should not) have such attribute, then the text is displayed at the size set for the field instance - and I don't know of a way to retrieve this programmatically.
View menu, Formatting Bar (status area doesn't even need to be visible)
Retrieving data ...