Fortunately, the FDA is a government entity that makes a bunch of documents publicly available! Here are links to the FDA briefing documents that were used for approval of the
Pfizer,
Moderna, and now
Johnson and Johnson vaccines. These documents are dry and verbose and long, but they have answers to all the questions you've asked so far, and they're written in language that I think most people could understand most of (unlike what you'd find in a medical journal). You could probably answer most of your questions by reading the executive summaries, but detailed info about vaccine effectiveness is around the middle of each PDF, and
very detailed info about side effects is closer to the bottom.
Between all of these studies, there have been tens of thousands of people vaccinated with no major side effects from the vaccine. There also haven't been reports of anything widespread in the people who have been vaccinated so far—at worst, maybe 50 cases of severe allergic reactions in the US (which can be bad, but are easily treatable and are the reason why they make you stick around for 15 minutes after getting the shot). There's also a bunch of safety and efficacy data out there from Israel, which has vaccinated >50% of its population, but I haven't looked at it closely yet.