What is the role of oxygen gas in our cells?

It's all of the things that you said. It's rather complex, but you might want to look at Kreb's Cycle

In a nutshell, oxygen is the final electron acceptor in the respiration process, so yes it accepts electrons from the electron chain. It does not do anything with glycolysis, it doesn't produce CO2, and it doesn't split water. You can say it aides in forming ATP, but only in "cleaning" up after the process.

I agree.

Oxygen is the final electron acceptor from the electron transport chain (ETC). It combines with two of these and 2 protons (H+) to form water.

ATP is formed through ATP synthase which couples the energy of a proton gradient to the phosphorylation of ADP:

ADP + P ATP.

That proton gradient is created as electrons move down the ETC towards oxygen.

Oxygen is never a catalyst anywhere, that's the job of enzymes which are complex proteins.

CO2 is produced by the cleavage of a C=O-O group (carbonyl) from two molecules, isocitrate and ketoglutarate, during the Krebs cycle and also from Pyruvate during the linking reaction.