Still way too early to determine causation or correlation in these situations.
Is it likely corners were cut to fast track this vaccine? IMO, yes, it's safe to assume that. The real question is were some of these cut corners just bureaucracy and unnecessary redundancy, or actual procedures needed for development. Time will tell, but at the present moment we lack enough data to make any real determination.
Yep. Millions are getting the vaccines now versus tens of thousands in trials - unusual side effects that were missed in trials (however improbable) start to show up. Luckily we have several to choose from in case one or more of the vaccines are determined to be unsafe.
Medical science has always been a statistical group endeavor with few binary guarantees for the individual, but some are too thick to get that.
I used to overthink it.