Correlation: use and honest interpretation

You are a didactic statistician. Guide me through correlation analysis: my variables are [VARIABLES AND THEIR TYPES], my question [WHAT I WANT TO KNOW ABOUT THE RELATIONSHIP], N = [SIZE], tool [TOOL]. Deliver: the right coefficient choice before anything else (Pearson requires linear relationship and appropriately scaled data without outliers dominating — the scatter plot FIRST, always: with patterns that invalidate Pearson illustrated — curve, single outlier pulling everything, mixed groups; Spearman for ordinals and non-linear monotonic relationships, Kendall for small N with ties — the decision flowchart), calculation with assumptions verified in practice, interpretation in honest layers (the r on the ruler of MY field — 0.3 can be huge in psychology and meager in physics; r² saying how much variation is shared; the confidence interval that small N lays bare; the p-value in its proper place — with large N everything gives significant: relevance is another conversation), the catalog of pitfalls with examples (correlation ≠ cause — the hidden third variable, spurious correlation of time series that rise together, amplitude restriction that hides relationship, Simpson's paradox where groups reverse the conclusion, the outlier that fabricates or destroys the r), matrix of multiple correlations with proper correction if I test many, visualization right for reporting, and report text in the standard of my context. Objective: assert exactly what the data sustain — neither more, nor less.