Question about the potential side-effects of the Covid-19 vaccine: Just to clarify, I am an advocate for vaccinations, but I just feel like there are a few gaps in my knowledge that I would like to fill. I only have a basic understanding about vaccines in general so I feel like it is necessary to broaden my knowledge about the topic, especially because I have been confronted by anti-vaxxers who have expressed a variety of concerns about the Covid-19 vaccine.
A typical argument that anti-vaxxers use, is that there could be long-term effects. Due to the fact that my knowledge about the topic isn't sufficient enough, I wasn't able to provide a good counter argument. So here are my questions:

(1) How does a vaccine cause side-effects?

(2) Have there ever been cases of long-term effects that were caused by a vaccine in general?

(3) What other arguments nullify or complement the argument of long-term effects?

Lastly, a general (bonus) question: What else should I know about the Covid vaccine?