I also have a glass-top stove at home. So far, I really like it: the heat is very even and there is good heat transfer, provided the pan makes good contact with the surface (one skillet I have has a bit of a lip, which makes it heat more slowly).
I've slapped skillets and pots full of water around on mine, and have yet to break it. I'm probably more careful than I would be on a metal range, but it seems sturdy.
But to your points:
1) There is no way cast iron could melt the glass. Iron melts lower than does glass (1200*C vs. 1500*C), so before you manage to melt your stove, your pan will be a puddle. It may, however, be possible to deform the stove top if you let an empty pan heat for some time. I don't see why this would be more of an issue with cast iron than with any other piece of cookware.
2) A heat defuser will work fine. Don't get the kind that is designed for use with gas, but anything else should work fine.
3) The burners on my stove are smaller than my skillet, so I find I need to move the skillet around to heat the edges. Also, flat-bottomed pans and pots seem to be much more effective on the flat glass top, as conduction seems more effective than radiation here. I polish the bottoms of my pots to get better heat transfer, although this is just me being anal.
Also: cast iron can't scratch glass. Glass is much harder than iron (see this wikipedia article), glass having a 6-7 on the Mohs scale, iron having a 4.
No, this isn't normal. A little flaking, perhaps, when you go over 600°F, but 500°F shouldn't do anything. It shouldn't even smoke.
Something is wrong with the seasoning on your pan. From the fact that its smoking, I'd guess its not sufficiently baked on. Alternatively, maybe the pan wasn't clean when you applied it.
If its just not baked on, I'd remove all the flaking bits (with some harsh scrubbing, sand paper even), clean it thoroughly, then bring it to around 300°F (stovetop or oven). This will make sure it is completely dry. Spread a thin layer of high-iodine value oil (flax seed is great, soy is pretty good and cheap and easy to find: look for the bottle that just says vegetable oil and check the ingredients, it's probably soy). Spreading is easy with a paper towel.
Next, toss into a very hot oven, 400–500, smoking is expected. Bake for 90 minutes, then turn the oven off. Allow pan to cool with oven. Once its cool, touch it. If its at all tacky, put it back in the oven, and bake for another hour (once again, allowing to cool with oven). It should be a shiny black at this point, and not at all tacky.
You can repeat the process to add more layers. Two should be reasonably non-stick to start cooking on.
If it still peels off after this, you're probably going to need to strip the seasoning and re-season the pan, after stripping it to bare metal. See What's the best way to season a cast iron skillet? to season it from bare metal.
Best Answer
The right way is simple and straightforward: preheat the skillet for about 5-10 minutes on medium, add a few table spoons of oil to coat the bottom, and continue cooking at this temperature. Flip regularly, to allow the sides to cook evenly, and wait for the middle to become fully cooked.
Now I will tell you all the ways NOT to cook a hamburger with a cast-iron skillet!
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