Important context for these materials: While the citing-in-LaTeX world has operated using BibTeX and natbib for a long time, these packages are no longer being actively updated. Over the next decade (and even if journals aren't there yet), the writing environment will shift to a biblatex regime. As of the 2nd version of biblatex, biber is the official parser for the .bib file — not BibTeX. This workshop operates on the assumption that the majority of your research writing requires a knowledge of BibTeX and natbib, but my goal is to also inform you about the future of citing in LaTeX.
These changes have very little impact on the .bib file (as of yet). A .bib file is still the preferred method for providing information about your references to biber.
Why are the session examples in ShareLaTeX instead of Overleaf? There are several different online LaTeX editing tools, including Overleaf, ShareLaTeX, and Authorea. The one a person uses really boils down to personal preference. ShareLaTeX is the most useful for teaching BibTeX because it doesn't auto-refresh the rendered PDF, and it lets you see the markup code really easily. Beyond teaching, Overleaf and ShareLaTeX are so similar that it's really about which interface you like more. You can find discussions on Reddit and the TeX StackExchange that weigh the relative merits of one or the other, but it's really a personal (and research group) preference.
Authorea is a different type of tool, and it focuses more on collaborative writing with the goal of submitting papers. It goes beyond just LaTeX, has some pretty cool features, and its UI is easy to use if you are collaborating with non-LaTeX users. However, Authorea has a cap on the number of documents you can keep private, so if you're looking for a place to keep your private collaborative course notes, your private research diary, and write papers for submission, Authorea is not the right tool for you.