Kitchen Safety – Is Glass Still Safe After Boiling Off Water?

Sometimes. Basically, this is the same as asking if glass is oven safe:

Generally, glass is oven-safe if taken from room temperature and put in a moderate-temperature, preheated oven. The key thing is to avoid temperature shocks (which will cause the glass to shatter). Some glass is specifically designed for oven use (either by being tempered or made of borosilicate glass). Often glassware will say if it is safe for oven use or not, and under what conditions—check the packaging or instructions it came with.

You also need to take precautions when removing glass from the oven. Do not set it on something that'll conduct heat away rapidly, such as a wet countertop.

Before heating glassware, inspect it for damage. Scratches, chips, etc. make failure much more likely. This applies to the microwave as well.

Note that non-glass parts of microwave-safe glassware may not be oven safe. For example, if it has a plastic lid, that should generally not be used in the oven (even though its OK in the microwave).

edit:

In response to your update, that oven is what would often be called a toaster or countertop oven. Those change temperature much more rapidly than a larger oven (which can be electric as well). So, generally, you'd avoid glass in them.

But, your glass says it can be used over a flame, from the freezer. So it's clearly one of the very shock-resistant ones, possibly borosilicate. I wouldn't expect it to be a problem. Just make sure to preheat the oven.

Also, since you know who made it, you can of course contact the manufacturer to confirm.

All cook top safety is the same:

Keep it clean and pay attention!

Glass ranges aren't inherently any more unsafe than a gas or normal electric range. Ranges are just a tool, one that generates a large amount of heat in a small area. Like any tool, you can hurt yourself or others if you don't follow the basic rules of use. Luckily, those rules are pretty easy to follow once you train yourself.

Keeping It Clean

When you are cooking, there is no reason to have anything around the range that you don't need to cook. No papers, no cutting boards, no wine glasses, no anything else. Anything extra is an invitation to spill or something to catch on fire. Nothing good can come of it. Cook with a towel and when you spill, clean it immediately. A clean range can't catch on fire because there is nothing to burn!

Paying Attention

Don't walk away from a range that is on! Almost every kitchen fire could be stopped by the simply having someone looking at the range when the fire started. You should be prepared with the failure signs for the type of cooking you are doing (like if your oil is smoking, you need less heat, or an open flame can ignite even low alcohol content if it's boiling).

If you follow those rules, you will almost never actually need this last one. I've worked professionally in kitchens for 14 years and I've only dealt with one fire that wouldn't have been stopped by the rules above. The final rule?

ALWAYS HAVE A FIRE EXTINGUISHER But it sounds like you already have that one covered.

In case SAJ in the comments is correct and I misinterpreted the question, your range is safe to continue using as long as you didn't crack the cook top or short the burners. The top is sealed, so you shouldn't see any particulate under the glass. If you do, you need to clean the burner assemblies before running current to them. That means wires and the infrared bulbs. Some brands will require this to be done by a trained technician. If the top is cracked, you need a new top, as the crack can redirect the heat or shatter.