Go read the question and answers email by Honeywell Now titled "Covid-19 Vaccine Questions and Answers" sent out on 12-21-2020, it might help answer some of your questions:
Q: Will HON require I get vaccinated before I return to work? What if I don't want to get vaccinated?
A: We have not made any decision on this point and will follow directives and guidelines established by local and national authorities as well as adhere to all local laws. The company will encourage employees to get vaccinated where they have access to safe and effective vaccines.
I suspect, if the vaccines ultimately prove to be safe over the long term, you will be "encouraged" to accept the jab by, first, not paying more for your insurance. If that fails to "encourage" you to comply, then it could become mandatory, especially if our tone deaf congress pass liability laws, similar to the liability protection the vaccine manufactures enjoy, that protect corporations from employees who are injured from taking the mandatory vaccine as a condition of employment.
I hope it all calms down soon. Very troubling times we are now living.