There are only handful of verified cases of people getting covid more than once. It's extremely rare from what I can tell.

Both are fairly rare, but the latest data I've seen shows both 1) weaker and faster decaying immune response in previously infected people vs immune response from vaccine, and 2) previously infected people getting infected at abt 2X the rate of fully vaccinated people. (Sorry, no ref links on hand at the moment)

Please post those links later when you get a chance

Here's a few:

Johjns Hopkins: Why COVID-19 Vaccines Offer Better Protection Than Infection https://www.jhsph.edu/covid-19/articles/why-covid-19-vaccine...

NIH: How Immunity Generated from COVID-19 Vaccines Differs from an Infection https://directorsblog.nih.gov/2021/06/22/how-immunity-genera...

Also, preprint on kinetics of regular infections vs breakthrus, showing vaccines rapidly suppressing viral loads - "Virological and serological kinetics of SARS-CoV-2 Delta variant vaccine-1 breakthrough infections: a multi-center cohort study" https://www.medrxiv.org/content/10.1101/2021.07.28.21261295v...

Most illustrative is the chart on ~pg16, line 298.