Paramagnetic molecules are molecules that have single electrons. When I draw the lewis structure of $\\ce{O2}$, it appears to be a diamagnetic structure. What makes it paramagnetic?
This phenomenon is explained by s-p mixing. All the elements in the second period before oxygen have the difference in energy between the 2s and 2p orbital small enough, so that s-p mixing (combination) can occur lowering the energy of the σ (2s) and σ* (2s) and increasing the energy of the σ (2p) and σ* (2p) molecular orbitals. By moving towards right in a period, the s orbital gets more ...
So why is molecular oxygen $\ce {O2}$ more stable than the molecular ion $\ce {O2^2+}?$ One possible reason that comes to mind is that the antibonding (AB) orbitals, although higher in energy than the constituent atomic orbitals, are still negative in energy, so adding electrons to AB orbitals still lowers the energy.
Likewise $\ce {O2}$ is as much oxygen as atomic oxygen is. The only complication is that what we habitually think of as oxygen is oxygen as a gas comprised of $\ce {O2}$ molecules. Like Humpty Dumpty in Alice in Wonderland, "a word means what [we] choose it to mean" and often we have to add modifiers or alternate terms to avoid ambiguity.
5 Why is the melting point of nitrogen ($\ce {N2}$) greater than that of oxygen ($\ce {O2}$)? After all, both are non-polar, and $\ce {O2}$ has more electrons than $\ce {N2}$. In addition, why is the boiling point of both opposite?
Paramagnetism is a consequence of having one or more un-paired electrons in the outer electronic configuration. e.g. O2, and NO. Most phys. chem. or inorganic chemistry textbooks will explain this in detail.
I think you are confusing something here: Molecular oxygen is most commonly found as the gas we know, $\ce {O2}$ and ozone, $\ce {O3}$. However, this doesn't limit it to only that. Oxygen can appear in a wide variety of (bio-) chemicals and there, it only needs two bonds to other atoms (or a double bond to one atom). Good examples for this are: The aforementioned water $\ce {H2O}$ where the ...
$\ce {O2 + 2e^- -> HOOH}$ 2) From the above we can deduce that water is the product; water is pretty stable in either acidic or basic medium - i.e. it won't react to a large extent with either hydronium or hydroxide ion.
