Oh, it is proven that the vaccine does not prevent one from contracting Covid because many people who were vaccinated have subsequently gotten Covid. What the vaccine does is "reduce the probability" of contracting the disease. I think there are data and analyes showing this. If not, it wouldn't be that hard to produce.

Just like with flu shots. Some people with flu shots do get the flu, but most people with flu shots don't get it.

Because correlation does not prove causation, in the case of the King County cardiac incidents more complete data and analysis would be necessary to establish any kind of proof. Often clear proof is impossible to obtain, so math oriented folks use the available data to perform a means squared analysis, or linear regression, of two or more variables. If the R-squared value is 0.9 or greater, most statisticians accept the correlation as causation.