Earlier quoted context omitted.
Coronaviruses are called so because they look a certain way under an electron microscope. They don't necessarily have common proteins. So you point a does not stand. As for point b,due to the fact that antibodies are specialized and there are tons of viruses that cause the common cold, I wouldn't expect them to match or even exist at any given time in the bloodstream since they only last ~6m and after that memory tak…
There is documented cross-reactivity in T-cell responses: individuals who had not come in contact with SARS-CoV-2 developed an immune reaction (T-cell based) against it. Whether this prevents infection (unlikely) or lessens the symptoms is still an open question. But the phenomenon exists.
Yes my impression was that it lessened infection, not prevented it, otherwise it would basically represent a vaccine or an alternative, at least for otherwise healthy people.