Congratulations, you are learning that these issues are not simple and there is not a single answer that covers everything.
You need to be careful in interpreting significant results when the researcher has unlimited degrees of freedom in the tests that they can do. There are arguments that you should adjust for the potential number of tests that could have been done, not just the number that actually were done.
If you keep adding tests, then eventually you will find some analysis that is significant, even if there is no real relationship. This is easy to see by using your favorite statistical package to generate 20 columns of random data with no planned relationship (generate each column independently of the others), now compute all the pairwise correlations and test if they are equal to 0. The truth is that the population or process correlations are all 0, but it would be very unlikely to not find at least one significant when looking at each test. So the adjustment idea is to take into account the number of tests. Now consider, what if you don't do all the tests, but first do a scatterplot matrix (look at all the pairwise scatterplots) and find the pair that looks to have the strongest relationship and only test that one pair. Now I have only done one actual test, but since I could have done all the others, the most accurate result would still adjust for all the tests that I could have done, but did not do.
A realistic concern is that if I am the manufacturer of Drug A and want to compare it to drug B, so I do a large randomized trial where patients are randomized to drug and at the end I see no significant difference between the 2 groups, but I still want to sell my drug, so I start looking at subgroups, is drug A more effective in Males? Females?, Older Patients? Younger Patients? Red Haired Patients? Green Eyed Patients? etc. If I analyze enough subgroups, I will eventually find something significant by chance alone, akin to the random example above. If I look at plots of the data, or other summaries, I can reduce the number of actual tests (and therefore how many I adjust for).
On the other hand, if I am now looking at side effects and my initial test shows that there are more deaths in the group receiving drug A than in the group receiving drug B, with a p-value of 0.02 (assuming traditional alpha of 0.05), but I don't want to share that. So I start adding some more tests and find that the rate of drowsiness is not significantly different between the 2 groups and the rate of rashes is not significantly different. So now I combine all 3 tests and adjust for multiple comparisons and report no significant differences in side effects now. Here the adjustment has benefited me as an unethical advertiser.
One approach to deal with both of the above problems is to preregister all planned analyses and to not do anything that was not planned ahead of time. More realistically we state the planned comparisons and report on those, but then also do exploratory analyses beyond those, but those results are dubbed "Exploratory" and used to generate new studies, not as final answers.
But what if death was not one of my planned outcomes, but the data safety monitoring board points out that there are significantly fewer deaths in the treatment group than the control group? This would be an exploratory outcome, but do we have the equipoise to start a new study looking at death as the outcome and randomize subjects to control?
You can see a lot more discussion on some of these ideas by doing an internet search (google or other) on "Andrew Gelman garden of forking paths".