It shouldn't. I haven't tried in 5600, but it worked fine in 5384. I don't
think it's neccessary, but if the installer doesn't tell you you've already
got a more recent version then go ahead.

If you want to be safe, create a System Restore point before the
installation. It's available under the start menu; just search for "System
Restore" and select Open System Protection (You can also get there from
Computer Properties > System Protection).

DirectX 9 is already included.  However some games (Battle for Middle-Earth
and quite a few others) may require you to install the version of DirectX 9
on the disc (else be greeted with an error about a missing d*.dll file).  In
which case there should be no issues with doing so.