If you're using the IDE like CS4 or CS5 there are some menu options to do this. I only use a text editor and Flex SDK to compile. While I know what you're talking about, I can't really answer this one since I don't have the program. There's plenty of tutorials on the subject, however.
I believe the path-following tools in CS* only follow (x,y) coordinates. No Z values in the menus, but you can code them yourself. Again, I don't have the program, but from the tutorials I read it looks like no.
I suppose it could. Instead of a line drawing like you have here, you could simply use an image of one rope segment (as in a picture of rope whose length is equal to one twist of the rope), then apply transformations to get the correct 3D perspective.
Basic flash programs only draw fills. You can, however, run a shader program (called pixel bender) within flash which will draw strokes for you.
Not on it's own, no. But there is nothing stopping you from programming your own decorated brush class.