My new menu item is showing as the first option. Is there a way to order where the menu item is listed. I would liek it last on the list.
Not really. The order is basically when the menu item was added through API. You can try ordering CB Auto Actions as the last plugin in CB > Plugin Management so it is always done last, but there's no ordering API or anything of the sort to determine what order they render in.
Also, Is there a way to have my new menu item only show on the viewing users profile...like the "Edit Your Profile" link does?
You can try making sure the displayed condition isn't empty, which is only set when viewing a users profile. Example condition as follows.
[cb:userdata field="user_id" user="#displayed" /] Greater Than 0