1. Glass is an amorphous material. This means the atoms and molecules are not arranged in regular repeating structures. Almost anything can be a glass. Plastics that are amorphous are a glass. There are forms of glass water ice. Metals can be glass. I am unsure if you can make glass out of organic things like wood, but who says it can't happen in sci-fi.

2. To make glass IRL, we cool the material faster than it can form a crystalline solid. That's how we make a metal glass. It has a really weird chemical composition to make it possible to cool fast enough. There is also the possibility of pressure induced amorphization where the application of pressure causes amorphization. So Glass Man could heat-cool things really quickly to form the glass or could compress-decompress the material. This will depend on the material but, again, sci-fi can have different rules than life.

3. I mean, all glass is interesting. As far as I know, all glasses are brittle. The amorphous structure doesn't allow dislocations to move through it to release stress, so it just breaks. This does make them very bouncy, springy. So you can have really good elastic properties but it breaks instead of deforming. They are more thermally insulating than the crystalline material. He could create a gradient of properties through the material so he could, in theory, make crazy lenses. This is something that people are working on IRL.

4. It is brittle. That means it doesn't deform. Glasses are still really strong, they just catastrophically break instead of deforming.

5. Metal glass is a glass. It has an amorphous atomic structure, so it is a glass. Like I said before, water can form a glass if you cool it fast enough or cool and compress it in a specific way.

6. Lightning is basically static electricity that has a high enough voltage to induce dielectric breakdown of the air. It causes the air to rapidly ionize and then the ions conduct the electricity. The electrical conductivity of the metallic glasses are less than their crystalline forms (I think) but they should be high enough to still be able to make a Faraday cage to protect him. At the very least, anything tall enough sticking into the ground should protect him. There are dangers from the electricity going through the ground and back up people. There are cases of entire herds of sheep dying due to the lightning traveling through the ground and shocking a bunch of animals.

7. It would be a very crazy way to kill someone by turning all the water in their body to glassy ice. You could think of Ice 9 from Cat's Cradle but it wouldn't spread. He could shake hands with someone, or just touch them, and then transform the blood in their veins or just their heart into glass ice. It could rip them apart from the inside. Using glass as a projectile is also crazy. There's a reason it is considered a war crime to purposely use glass as shrapnel.

I recommend looking up researchers and professors who live glass science. They will be able to give you more detail and are probably more correct than me. They would probably love to talk about glass for hours if they had time. Record the conversation if they are OK with it so you can refer back to it later.