I’m definitely in the pro-vaccine, pro-mandate column, but both 1 and 3 from your list strike me as dubious given the information to this point. Certainly there’s been conflicting information on both.
Re-read my comment. I'm asking if anybody downvoting me can provide scientific evidence that those statements are true. Nobody has, because they're not.
Natural immunity is durable and robust, and vaccinated people can get infected and spread the virus. In fact, according to the Israeli data, vaccinated people are magnitudes of order more likely to get a Delta breakthrough infection than a person with natural immunity is to get reinfected with Delta.