Yes, even if you have a good correlation, you should still test for autocorrelation and outliers. You want to make sure that you either didn’t find a spurious [false] correlation or that your correlation wouldn’t be even stronger without outliers or without autocorrelation. I always perform these 2 checks when I run regression analyses (as well as a few of the other ones you saw in the course).
From what I’ve seen in practice, assuming that good results are necessarily right is a frequent pitfall of even experienced data scientists.
Yes, I’ve given a Simple Linear Regression example to a couple of Data Analysts, and they seem to skip the autocorrelation test, in fact, they seem to depend on X and Y correlation R-Squared, and charts only.
A professor told me that I should find out why there is autocorrelation in the residuals. This makes sense but I am not really sure how to go about it given a domain I am not really familiar with.