In general (at least from when I last kept up), new parts are introduced when LEGO introduces a “theme” of several sets with a similar aesthetic or subject matter at a time. The vast majority of parts appear in multiple different sets, though there can be a few more rare and unique parts. I’d assume that in general once LEGO makes a mold for a part they’d want to re-use it on parts for multiple sets. Rare and unique printed patterns (or if the company is being lazy, stickers) on standard parts are more common than unique part forms.
For seeing which pieces came in which sets I used to use Peeron™ LEGO© Set Inventories, which looks like it hasn’t been updated since 2012. BrickLink Appearance In Inventories also has what might be a more recently-updated directory where parts can be looked up (to see what sets have them) if you retrieve their numbers from another page (like the set listings) on the site.
I don’t remember any site offering good statistics about sets that I saw in my past experiences. https://brickset.com/ looks like it might have a few set-specific curatorial guides, and Rebrickable | Rebrickable - Build with LEGO looks like a new site focused on sets which I haven’t heard of before.
In general the parts are very interoperable (though there’s plenty of really obvious and intuitive limits like pole-based pieces w/o stud holes, such handheld objects, being able to connect with say open studs or hooks but not solid studs), but there have been edge cases of “illegal” builds identified where certain combinations can put excess stress on the pieces, provide inadequately secure connections, or in some cases even be relatively irreversible combinations, and IIRC the company doesn’t authorize doing them in official sets. Here’s a PDF that’s from back in 2006, but it’s nicely documented: http://bramlambrecht.com/tmp/jamieberard-brickstress-bf06.pdf (Also had an HN discussion: “Illegal” Lego Builds (2006) [pdf] | Hacker News) SNIR in general may be kind of on the “illegal” side of things from the company’s point of view, though I haven’t looked into it. I also IIRC remember reading about how LEGO’s manufacturing quality is/was very high, and that might factor into them setting standards for legal moves to not impact their high expectations of long-term durability.
Also another building technique I forgot about: in addition to SNOT/SNIR, there was also a “studless” building trend where builders tried to cover up every stud on their models with plates and/or sideways construction. I thought it was particularly elegant when done well, and there were some neat builds particularly among the community of people building space-related creations. Paging through the archives of https://news.lugnet.com/space/moc will probably reveal some neat approaches.
I’d guess there might be some kinds of existing online guides and resources on Reddit or somewhere specifically for adults returning to LEGO, or adult beginners. The term I used to see used for people getting into LEGO again as adults was that they were returning from their “dark age” where they stopped playing with it between childhood/the start of adulthood, so that could be a possible term to search for.
(Edit: another interoperability issue I just remembered: the early 00s controversy when LEGO made the color of grey they used slightly different - slightly bluer - from before, so new/old bricks no longer exactly matched in color. There was a big uproar about that from adult customers, which the company made statements specifically in response to. The term fans used to criticize the new color at the time was calling it “bley.”)