I'm not an expert, but it sounds like you have what we have at our house, so I'll say what I know (and/or can reference).
From Wikipedia: "The forms are interlocking modular units that are dry-stacked (without mortar) and filled with concrete. The forms lock together somewhat like Lego bricks and serve to create a form for the structural walls or floors of a building."
In other words, no wooden studs. Just plain ol' styrofoam.
If you're able to look at the top part of the wall, you might actually be able to see the protruding Lego brick-like top part of the interlocking structure. This would also tell you just how thick the form is.
While Wikipedia says the form bricks are dry-stacked, it wouldn't surprise me if there were a little adhesive used between them (it kind of seems like a good idea, but it's possible the form manufacturers recommend against that for some reason).
As far as how they attached the drywall: just a bunch of screws, in our case. It's also reasonable to use adhesive in addition, as long as it won't eat through the styrofoam (or other material), of course. The styrofoam was actually surprisingly strong when I was drilling screws into it. Given that they used somewhere in the neighborhood of 20 screws on the 4' wide floor-to-ceiling sheet of drywall, I have no concerns about it coming down.
There are electrical outlets and phone jacks on our ICF walls, and the lines and boxes are accommodated by carving out appropriate cavities. That creates another factor to consider when drilling into the ICF wall. Specifically: how straight are the channels that were carved out, and in which direction were they carved? Did they use nail plates along the route?
Now, as far as attaching things to the wall securely is concerned... I doubt it would be equivalent to a stud in terms of support capacity, and I'm having trouble finding information on this topic online. If the drywall is attached directly to the ICF, you won't have any cavity behind the wall to place a spreading-type anchor, so those are ruled out. Of course, if you make the assumption that the wall is at least as strong as drywall on its own (indeed, I'd assume it's at least a little stronger), you can use a self-drilling drywall anchor (Lowe's has one branded "TOGGLER") and get plenty of capacity. Plus, you can use them in any location (excluding wire runs, as noted above) without worrying about hitting a stud after you've bored a giant hole in the drywall.