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.
Best Answer
If your alternatives are an oven or non stick pans, these sit perfectly in the middle. They really shine at high temperatures, and with marinated foods.
I personally mainly use mine for meat, as my SO is vegetarian, and doesn't like their vegetables cooked in a meaty pan. However it also works nicely for bread products. I toast my burger buns in it before making burgers, my flatbreads when making kebabs, wraps, naans, all these get a nice toast with grillmarks when I use them. It adds a nice partial char to the food that you can't get another way without burning larger parts of your bread.
You can use it with vegetables as a low-fat solution to frying, or use it to make nice smokey gravies.
However where it really sings is indeed with meat. It can go up to soaring high temperatures, where non-stick pans tap out long before. This is ideal for cooking steak in particular, but also smash burgers (they are thin and need the outside cooked fast if you want any kind of darkening). It is also ideal for cooking anything marinated. If you use a pan or broiler, it could char and burn large parts of your marinade, especially if you use herbs. With this grill pan, it will only burn (char) the lines, and steam in between leaving the dynamic of your marinade intact.
The only downside I have found for this kind of pan is the maintenance. It should be kept well seasoned like all cast iron pans and woks. After cooking, clean it by adding one or two pints of water and a teaspoon of salt, and simmer for 15 minutes to an hour. This will dissolve the non-oil particles and leave the non stick seasoning intact as opposed to using soap. Then dump out the water and wipe the pan with paper towels. (Note: I have found that different foods need different simmer times. Breads need next to no cleaning, and fatty means tend to clean up quite quickly. Leaner meats like chicken etc. tend to get charred more and stick to the pan, and will need longer simmer times - yes, up to an hour - to loosen up, even in a well seasoned pan.) It also gives off large amounts of smoke and steam for an inside pan, and you will need to have your extraction fan on high and preferably a window open as well.