Open appliance which has a flat round disk as a screw head, no recess at all

Whatever it is, it's made not to be opened - why are you trying to open it?

Rivets seemed like a good bet at first, but I'm now inclined to say the "snap off" as mentioned by @keshlam - a screw engineered so that the item can be assembled, and then the means of turning the screw can be broken off (leaving the non-soft hex scar)

You could probably grind a slot into them if you really cared to waste the time, and didn't mind damaging the plastic somewhat. At a higher equipment and skill level, if you have or get the type of bit that uses two pins to engage two small holes (USA use is spanner, but in the UK that's just a wrench, AFAIU), you might be able to drill those two small holes, though you'll likley need a above-average drill bit (the heads may well be hardened)

Those could be screws with the heads removed, specifically to prevent people from opening the device. In that case, try to cut a slash across the top of the screw so that you can get a flat-head screwdriver in there. A dremel comes to mind, although you'll damage the plastic casing, but, hey, if you want to make an omelette...

Just as likely though, they are like ring-shank nails, with notches on them designed to catch on the plastic inserts on the other side and ensure that they never, ever get removed without destroying the device. In this case, the answer may be to drill the head off of them so that the shank can be pulled through the hole in the plastic. Understanding, of course, that you won't be able to put them back together.

Why do you want to take it apart, incidentally?

Hope this solves it for some of you. So, is it a screw or a stud? Well, I cut a couple open to see. They all seem to be screws, in my case. It’s hardened steel so I wouldn’t waste time drilling. I’ve managed to actually remove a few now very easily using a drill-bit upside down with a drop of glue. Works best if you use a bit the size of the head. Press down, not too hard or fast, and set drill to reverse. Viola! Replace with regular screws. If you don’t have a drill you could try an old screwdriver cut off at the shaft and sanded flat. It even works with an Allen key/wrench. Good luck.