Also, during the H1N1 scare a vaccine used in Europe caused some people to develop narcolepsy (though perhaps more would have gotten it from the virus itself without a vaccine). It can be hard to determine that something is “safe” quickly.
SARS-CoV-2 is also at a really awkward point in the fatality curve (with the best estimate of the IFR being around 1%) that you really want to do something, but you also can't really accept a significant chance of that something having a significant side effect.
Yes. In some cases, the wrong kind of immune response can cause antibody-dependent enhancement (https://en.wikipedia.org/wiki/Antibody-dependent_enhancement), where the immune reaction enhances the severity of the virus.
This is not terribly common, but alas this exact mechanism has been seen in earlier work on SARS.