It’s various combustion products (which will vary depend on what is being burned)–in the case of hydrocarbons, these will include CO2, CO, water vapor and who-knows-what-else. It glows because it’s very hot. Hot atoms and molecules slam into each other with enough energy to emit a photon, the color of which will depend on temperature and/or the chemical composition of the hot material.
In a manner of speaking, yes. The dynamics are a bit complicated, but basically, the gas cools off to a point where it no longer glows in the visible, although it’ll still radiate in the infrared. Viewing in the IR, the flame would appear much larger.
IANAScientist or anything resembling one, so please wait for confirmation from minds brighter than mine to take this for anything more than a WAG.
Fire, as we observe it, is two main things:
1- a mixture of the substance that is being burned and whatever that reaction gives off (Wood + Oxygen -> ashes)
2- energy, which we see as light and feel as heat.
Heat. Anything heated enough will glow, with a colour matched to the temperature - this is where the phrases red-hot and white-hot come from; it doesn’t matter what the material is, if it’s heated sufficiently it will glow. Flame is merely ANY gas put off by the burning material heated to the extent that it glows; being gaseous it is free to dance around whereas a red-hot poker is not.
What about water? - I acknowledge the basic truth of your answer, but I’m just curious as to how water might be rendered incandescent. Is it possible to heat water (well, steam) to an incandescent state, without turning it into something other than water?
Sure. It’s doing it right now, in fact. Anything above absolute zero (which is to say, anything at all) will glow due to its temperature. The hotter it is, the shorter the peak wavelength, and the more energy will be released at each wavelength, but it’ll always glow some. If you have something around room temperature, it’ll glow mostly in the infrared. Get something (like an electric stove burner, for instance) up to a few thousand degrees, and it’ll start glowing in the visible and be red-hot. Get something (like, say, the Sun) up to about 6000 degrees, and it’ll give off enough light in all the visible colors that it’ll appear yellowish white. People often think of infrared as “heat”, since that’s the color given off by most objects we’re familiar with (like, say, people), but it’s the exact same process which causes people to glow in the infrared as causes the Sun to glow in the visible.
Now, if you’re asking “hot enough to produce a significant amount of visible light”, that’s possible, too. The water won’t be liquid any more, of course, but water molecules are observed in the upper layers of some of the cooler stars (those which are merely red-hot). As a matter of fact, water is one of the substances which can be heated the most, without breaking down: Mostly all of the molecules you’ll find in a star are simple things like water, carbon monoxide or dioxide, hydroxyl, and cyanide.
If flames are conductive, then passing a current through them should generate a magnetic field, with which another magnetic field could interact so as to confine or move the other. I may be on the verge of inventing a candle-powered plasma beam weapon.
Flame rectification, a technique used in heating furnaces, among other applications, to detect if the burner is lit:
It should be noted that the ions the article mentions are actually produced by the applied electric field, rather than the process of combustion itself. So, yeah, a flame is weakly conductive, but not because it’s a plasma. It can become a plasma under the right conditions, though. Put a lit birthday candle in the microwave, and you’ll see. Use an oven you don’t care about–it will scorch the inside of the oven.