[mcgsxr]

I have secured an older Dell SFF PC to use for my audio system, via ethernet to SB3.

The PC is running headless (I boot it and the USB drive when I want to listen to the system, and turn it all off afterwards).

I am using an offboard USB drive.

When I use a USB drive on my normal PC, the drive wants to autorun or autoscan when I turn it on.

How can I stop this from happening?  Does it matter?

Is there a way to connect to the headless PC via wifi?  The SB3 can act as a wireless bridge, so if I can leverage my existing VLAN, that would be useful.

There is no room (or budget) for a monitor at present, as all the gear is living in this old stereo unit, across the basement from my system.

[Rashiki]

When I use a USB drive on my normal PC, the drive wants to autorun or autoscan when I turn it on.
How can I stop this from happening?  Does it matter?

Use Linux rather than Windows. 

Yes, there is a way to turn off autorun. Check out this link: http://www.tildemark.com/tips/disable-autorun-on-cdrom-or-usb-drives.html

Is there a way to connect to the headless PC via wifi?  The SB3 can act as a wireless bridge, so if I can leverage my existing VLAN, that would be useful.

Look into using VNC. There's a server and a client. You run the server on your headless PC and the client on another computer.
There are many implementations of VNC. Here's one: http://www.tightvnc.com/

 -Rob