Of the 4 points you mention you've seen, I'd say the only one that's entirely incorrect is #3.
1. Only use H1 once: True. Think of it like a book title. That's the most important thing, so nothing else should share that prominence.
2. H1 is crucial for SERP: **True. **This is what Google looks to, after your title tag, for information about your page and the content therein. This reaffirms that your metadata, keywords, title, content, etc. are all related - while also showing visitors what this page is about (Google values visitor experience more and more with each update).
3. Use H1s for subheads. False. Think back to #1 - H1 should be reserved only for the 1 absolute most important thing (which should be your title).
4. Google almost never looks past H2 for relevance. Kind of true. Google DOES look beyond this (and even parses your body-text), but with each lowering of prominence / heading, Google gives it less weight. #4 is true in the sense that this weight is lessened significantly, but it's incorrect generally - your content is still very important.
I hope this has been helpful to you! Good luck!