1. Good question about popcorn. While visible light does have higher energy than microwaves, for a material to absorb energy, a condition called resonance must be met. A simple example of resonance would be from recognizing that different colors of light possess different energies. Red light is absorbed by a green material because there is a resonance condition between the color of the material and the color (energy) of the light. Green light has higher energy than red light, but green light is not absorbed by a green material (and thats why its green). Similarly, while the water in the corn has a resonance condition for absorbing the microwaves (which it does and therefore heats up), there is no resonance condition for the corn to absorb visible light and turn it into heat.

2. When a gas is tuned into a plasma, the change is more like a temporary chemical change (the gas is ionized with electrons being removed from atoms) rather than a physical change. There is therefore no equivalent of "melting" or "boiling" for the change between a gas and a plasma. One could use the term "ionization" but this should not be compared with "evaporation".

1. The issue here is the distinction between energy of a photon (indeed microwave photons have lower energy) and intensity (i.e. number of photons). A typical 100 Watt light bulb delivers only a tiny portion of that energy as visible light.. (Less than 1%).
On the other hand, atypical 900Watt microwave oven uses 1200W or power and delivers about900W of microwaves. Some years ago I used a CO2laser delivering about 150W to cut sapphire substrates. It sliced the material, about 2mm thick and nearly as hard as diamond at about3 inches per second...
Part of the issue is that visible light sources are very inefficient --even LED's are only in the 20% range, at best.
2. The phase change from a gas to a plasma is called ionization -- which refers to the stripping of some electrons from the neutral atoms. The term predates the concept of thinking of plasma as a fourth phase of matter. I don't know the term for gas condensation from a plasma.

Turning a gas to a plasma is called ionization, and the reverse process is called recombination.

A gas can become a plasma even if only a fraction of its atoms lose electrons. The essential feature of a plasma is that it has enough electrons and positive ions flying around to be electrically conductive (whereas gases are good insulators). Plasma's conductivity makes it behave differently than gas in other ways, too. For example, plasma is bound to magnetic fields and can carry magnetic fields with it, but ordinary gases have no interaction with magnetic fields.

Plasma is actually by far the most common phase in the universe. Stars are made of plasma, and most space "gas" is actually plasma. There are many other phases besides the basic four: Neutron stars are made of "degenerate matter", which is as dense as an aircraft carrier in a cigarette lighter. Super-cold helium can become "superfluid", which means it can do a whole bunch neat tricks (like escape containers by climbing the walls). Some materials have a zoo of phases between solid and liquid, collectively called "liquid crystals".

1. It's an absorption feature problem. The size of the electric dipole of a water molecule is on the same order of size as the wavelength of microwave light,making water molecules perfect antennas at that frequency. As a result, exposing water molecules to microwave light will cause them to spin, generating friction, and thus heat. Shorter wavelength light cannot cause water molecules to spin like that since they are too big, and longer wavelength light cannot impart enough energy, although they can on a longer antenna (e.g. radio waves excite a radio antenna).

2. The transition from gas to plasma is called"ionization" (the particles that make up a plasma are ions instead of molecules). I don't know if there is a word for the reverse, but "molecularization" is probably reasonable (gasses being composed of molecules).

What, aren't you satisfied with how microwave ovens work? Here are some problems with building an optical wave oven to consider:
1) Microwaves mostly interact only with the water in food. An optical wave oven would interact with just about everything in some way. So everything gets really hot. Also, optical probably wouldn't penetrate as easily into the food as the microwave does.
2) I don"t think anyone has made a way to generate optical power the way we can for microwaves. It would have to be something like being inside the tube of a high power laser.
3) How do you build a box to contain all this optical energy?

I think you would call it "ionization" as the process of going from gas to plasma involves ionizing the atoms or, in other words, separating electrons from the atomic nuclei. The name we use in my field (astrophysics/cosmology) for going from ionized to neutral gas is "recombination." A quick search on the web tells me that plasma physicists probably use these terms also.

Microwaves do have a longer wavelength than visible light and that does mean that they have a lower energy. Microwaves are able to pop the popcorn by disrupting the rotational motion of the water stored in the popcorn kernal. By disrupting this motion, the water starts to move around faster and eventually pressure build will pop the kernal. I also believe that microwave light is more intense than visible light. By this I mean that if you were to increase the intensity of visible light, such as having a certain amount of visible light brought down to a point source like a LASER, than you would be able to pop the popcorn.

You are absolutely right about the relationship between wavelength and energy. If you want to heat something up by bombarding it with radiation, then ultraviolet light will work better than visible light, and you'll be sitting around forever waiting for your popcorn if you use infrared light or radio waves. This kind of heating works just by increasing the velocity of the molecules in the object. Luckily for the shareholders of General Electric, there's more to it than that.
What you have to know is that different wavelengths of light have different effects on individual molecules. UV light has enough energy to break chemical bonds, which is why you get skin cancer -- UV from the sun breaks bonds in the DNA of skin cells. Visible light can't break bonds, but it can knock electrons up to a higher orbital state -- chlorophyll, retinal, and other pigments work by changing their shape in response to this kind of electron movement. Microwave radiation is too weak to do any of those things, but what it can do is cause polar molecules to isolate. You probably know that water is a dipole because one side of the molecule has nonbonded electrons orbiting the oxygen atom (and is therefore slightly negative), and the other side has the two hydrogen atoms that are somewhat positive because the electrons 'shared' between the O and H atoms spend more time orbiting the large O nucleus (which has lots of protons) than the small H nuclei (which have only one proton). So the water molecule is very much like a small magnet with a + pole and a - pole. If you put this dipole in a magnetic field it would orient itself along the magnetic field, just like a small magnet moves if you hold it near a large magnet. If you put a dipole in an oscillating magnetic field of the right frequency, the dipole will oscillate, too. Well, waves of electromagnetic radiation have that name because they're made of an oscillating electric wave and an oscillating magnetic wave. And it happens that the microwave radiation we use in microwave ovens has a magnetic component with precisely the right frequency to cause water dipoles to oscillate. So you put a glass of water in the microwave oven, and the microwaves start flowing. The microwaves cause the water molecules to start oscillating, and this oscillation heats up the glass of water.
The microwaves don't make molecules move around and heat up like UV radiation would, but it does cause molecular motion by making the water dipoles oscillate. As a result, microwaves only heat up things with water in them, so you can't heat up a brick in a microwave. Your kid sister's Easy-Bake oven with a strong lightbulb in it will heat up the brick, but it's going to take a lot longer to boil a glass of water!

As for your second question, I don't know of a name for that phase change. A quick look on the internet seems to indicate that there isn't a name for plasma-related phase changes. On the one hand this makes sense, because things don't change back and forth from plasma very often, so we don't really need a name for that. On the other hand, scientists love naming things, and we have plenty of fancy names that are perfectly useless, so it's sort of surprising that nobody has invented a name for plasma phase changes. So if you want a fun project, you should just invent a name for a gas-plasma phase change.
Post it on the internet, and the next time somebody is wondering what the name for that is, they'll find your name.
Bam -- you've invented a scientific term! Even better, you could find a physicist somewhere who works on plasma. Email him or her and suggest your term. If you get a physicist to start using your term, then it will definitely take off.
Either that or you'll find out what the real answer to your question is.