Plasmas are so hot that there is enough energy to strip electron from the atoms to make free electrons and ions. This is takes so much energy that it all bonds between atoms are broken long before you get a plasma. (There is enough heat energy to do this in a star or nuclear explosion, but in the lab we cheat by putting a HUGE electric field across the chamber and hit the gas with a laser to help pull the electrons from the atoms. I used to work at the LaPD which was the largest plasma device in the world in the 2001 and we would have to wait until night time to run experiments because we used 90% of the electricity available for the power grid serving UCLA and Bel air. If you want to read more here is the link.

So if you did put CO₂ in the chamber you would make a plasma that was C+ and O+ and electrons when it was in the plasma form and when it cooled might recombine to make CO₂, CO, O₂, and either graphite or maybe C₆₀. When a plasma cools, it is a bit like musical chairs and the atoms and electrons recombine in any way they can.

As for your second question, most gasses, including the helium, neon, argon etc. form solids above freezing. Helium gas that has a mix of isotopes (atomic mass 3 or 4) freezes into a liquid at 4K and will not freeze at 0K and 1 atm, it can be turned into a solid at higher pressure. The reason for this is hydrogen, though lighter, is diatomic and is much easier to lock into a crystal since you can't rotate in a solid, whereas helium is light and is mono-atomic, it needs to be pushed into a crystal at higher pressure. This is because you have only 2 electrons around the nucleus and they are held very tightly making He very small. To pack He into a solid the atoms need to be very close and the repulsion of the nuclei and the electrons keep the atoms apart even at 0K and 1 atm, you need to really push the atoms together to make them solid. Helium 4 isotopes do something very special at low temperatures called a Bose-Einstein condensate which is not a gas or a liquid but behaves in very odd way. It looks like a thick smoke but does not obey normal physics (it can flow up walls) since it is essentially a huge atom and so follows quantum mechanical rules instead.

A plasma is a gas that has absorbed so much energy that the outer shell electrons are 'flung' off the atoms so you can think of it as a swarm of positively charged ions zipping around incredibly fast in a sea of electrons so the total charge of the plasma is neutral, but almost all of the atoms are ions. Since this takes such a large amount of energy, compounds that contain more than one atom will be torn apart before the gas turns into plasma. Pure elements like gold, however, should in principle formplasma without decomposing.

Temperature is a statistical definition defined by how fast atoms or molecules in a material are jiggling about. In solids, the atoms jiggle very quickly back and forth but don't travel any actual distance because there are strong forces holding them together (coulomb's forces in the case of salts, Van der Waal's forces in other cases). Long story short, at absolute zero there is absolutely no jiggling whatsoever (if there was, it wouldn't be at absolute zero by definition) so any attractive force between the atoms/molecules would hold the material together and it would be a solid. As you get arbitrarily close to absolute zero, you will always form a solid unless there are no attractive interactions at short distances (which there are for all materials we have ever encountered).