Hello! From Arc's layout window, File => Export => file type AI should yield a scale and an extent indicator map in perfect vector format on their own Illustrator layers. It worked on my end. But, if you can't get that to work, consider the "Arc/Illy Cheat:"
Export the Arc layout as a pdf, and add it to an Illustrator layer called "Arc pdf." In Illustrator, lock "Arc pdf," then use Illustrator's tools to draw a more attractive scale on a separate, unlocked "Scale" layer. This retains scale accuracy, but addresses the aesthetic issue. Secondly, your extent indicator: I don't know why it doesn't work for you, but a workaround would be to generate an mxd which contains only those elements in the extent indicator window. Export that mxd by itself, and give it to the Illustrator coworker, who can scale it inside Illustrator to meet his/her needs. Also note that depending on the intricacy of the extent indicator map, it might be quite simple for the Illustrator person to digitize the extent manually.
