FDA drug testing is done in four phases:
Phase I - Tests basic safety, proper dose, and effectiveness with a small number of participants (typically under 100)
Phase II - Tests safety and effectiveness at the previously established "proper" dose and regimen with a larger number of participants (typically several hundred and up to around a couple thousand) with a wider age and ethnic range
Phase III - The final pre-approval phase, tests safety and effectiveness of the regimen with 30,000-60,000 participants with an age range that may or may not exclude children under age 12 and a full ethnic range
Pre-approval test phases are done:
* To protocols written by the FDA;
* Double-blind and with half of participants receiving placebos in at least Phases II and III;
* With an independent committee overseeing safety, having custody of data, stopping enrollment to investigate "adverse events" to determine if the event was related to the vaccine, and doing interim analyses of test data to see if the vaccine is effective, with the possibility of the trial being terminated.
Phase IV - Ongoing monitoring for "adverse events" among participants in Phases I-III and people vaccinated after approval; Phase IV is ongoing, probably for several years
That records are kept of people receiving vaccinations is normal, as a whole. Being a new vaccine, Pfizer's and Moderna's and etc.'s will be monitored in their respective Phase IVs. Recipients should notify their physicians, if that isn't part of the process of receiving the vaccination.
I doubt that any state will try to mandate universal vaccination. If a state tried it that law would probably be tied up in courts for, well, long enough for it to be irrelevant if the law were upheld.
NJ's hoped for 70% number is probably what their health officials think will, when combined with the number of people who have immunity due to having recovered from Covid-19, result in "herd immunity". After the Dems' anti-Trump-Vaccine campaign of this summer and fall, I doubt that 70% will be achieved.