first off, I'm not sure... but even if it did, I'm not sure that's the route you would want to take. There's not a gamepad in existence that could handle all the hotkeys and other button presses a typical high-end EQ player has at the ready.
We have Logitech Dual Action controllers on all of our computers, they work as intended. We use them all the time, although they deal with the more routine actions such as debuffing/nuking on alt characters. On Windows, it isn't so much "does a game support it" as whether it has drivers for your version of Windows since a lot of it is standardized. What you don't get is in-game specific control, but that hasn't been an issue for us. We can do whatever we need on the controller.
EQ itself does not support any gamepads. If the gamepad supports keyboard emulation, then you can definitely use it to do anything you want in EQ. In the past I had a few different gamepads which I used very well; all you had to do is set up the gamepad to use the appropriate key strokes to trigger whatever hotkey or command you want.
The short answer is "no". Is there any freeware utility that will make use of the two thumbsticks? For instance, a utility that can assign mouse motion to the right thumbstick.
As Borek said, the Nostromo (n50 and n52 both) were awesome with EQ. When they sold out, and the software for the new version of the n52 was crap, I ended up going with a Logitech G13, and I will never go back to anything else. One awesome feature of this device, is the ability to store profiles for games on the controller. Swapping between a desktop and laptop only takes seconds for the profiles to load up into the controller software.
Not sure how you came to this conclusion. As I posted earlier, it is dead easy to get a controller going when they are supported by Windows itself. We have used the Nostromo gamepads in the past and have since switched to the Logitech Dual Action on all computers, as well as Logitech G110 programmable gaming keyboards. The shortest answer is actually Y.