Nothing in science has meaning before replication. Look at cold fusion for a classic example where this rule was ignored. Of course, you may be speaking of the prevailing standards in psychology, in which case you're right -- but then psychology isn't a science.
> 2. Apparently the first study isn't science.
That's correct -- it isn't.
> I didn't realize that science was a catch-22 situation.
Only if you can't replicate any studies. That's psychology's problem, but not science's problem. In science, studies are replicated regularly, and no one takes a study seriously if it hasn't been replicated, especially where human health is concerned.
> They have a testable hypothesis: that acetaminophen/paracetamol has a side effect of X.
That is not an explanation, it's a description. Science requires testable explanations. The paper doesn't presume to explain its results.
If I say "the night sky is full of little points of light", that's certainly testable -- someone else can go outside the tent and confirm it, but it's just a description -- not a basis for science, which requires that someone have the nerve to suggest an explanation for what has been described.
But if I say "those points of light are actually thermonuclear furnaces like our sun, at greater distances", I have offered a testable, falsifiable explanation. That's science.
If someone correlated a specific biochemical action in individual neurons with later very specific behavior, that might count as science, but that would be neuroscience, not psychology. Psychology doesn't try to analytically connect specific physical causes to effects -- it's satisfied to describe outcomes without pretending to know why they are so.
> See https://yourlogicalfallacyis.com/
The fallacy is yours, not mine. You appear to think one study making ten claims constitutes science. In fact, science is ten studies making one claim.