Quote: "Will installing DX9 on a Vista machine still leave DX10 intact?"
Yes, DirectX10 and DirectX9 use entirely different draw systems.
You do have 10 and 9Ex installed by default; Games for Windows are compatible with those runtimes.
DarkBASIC Professional unfortunately is only compatible with 9.0c
So you will need the runtime for it.
If you play to run games using older apis (5-8) then I'd recommend installing them first and upgrading them, as you will experience better backward compatibility.
e.g. Dark Forces II Jedi Knight using the DirectX9.0c runtime just renders a black screen, uninstalling DirectX9.0c installing DirectX6 (from disc) then upgrading to 9.0c again and the game will run exactly as you'd expect it to.