Since you're in a dedicated aerospace program, you'll have a good base to do quite a lot in aerospace. I've seen a number of people coming from mechanical programs with aerospace options, and they usually have a lot of basic airplane knowledge missing.
1) Technical advances are moving towards more and more integrated analyses, and typically the flight simulation (we use MatrixX, but are going to Matlab Simulink). Obviously, separate analyses are still performed, as running a CFD module within the simulation would be sill right now (maybe in 20 years, if More's law holds up). In the physical realm, more electric aircraft are going to drive us towards more integrated solutions too. So, I'd say knowing controls will be in high demand (also consider UAV application)
2 )Certainly, but mostly within aerospace. Though I've heard that hard drive manufactures perform aerodynamic analyses, as I understand. Be prepared to run lots of CFD codes.
3) Typically, aircraft dynamics/ S&C and the control systems analyses are handled by separate groups. The distinction being the whole aircraft analyses, or individual system performance.
3b) I'm assuming that you didn't mean Loads & Dynamics. We look at the flexible body dynamics, and call any rigid aircraft motion static (quasi-static really). L&D acts as an interface from the aero/S&C/weights to the Stress group. Also included is the Flutter (aeroelastic stability) of the dynamics. Within L&D, we have aero, controls and solid mechanics specialists (myself mostly in the solid mechanics camp, and specializing in landing gear)
4) I guess that depends which control, but generally I'd say no. EE's have problems seeing anything other than electrons
It sounds like you are leaning towards controls, which is probably a good idea, especially since the applications outside aerospace are good. But as a past grad student at WSU, and KU BS grad ('90), my experience was that WSU was not that strong in the controls department. If you can take it as an elective, there was a good ME course, the book was "Computer Aided Analysis of Mechanical Systems." I'd recommend studying both control theory and the mechanical aspects of systems.
Also if you can get into the Co-op program, that's a good foot in the door. Learjet, where I started working in aerospace, should have some co-op openings. I know the last co-op in the performance group just too a job at company C.
The last important consideration. Where do you want to live? Something I never considered much as a student. but if your specialty is only suited for OEMs, that limits your choices somewhat. If you like Wichita (god help you), then you've no worries. I had to escape to Canada (Montreal).
