I've read the article on Moz's blog, "Are H1 Tags Necessary for Ranking? [SEO Experiment]"
Those are pretty high authority sites.
I am fairly familiar with Moz
And what about h3-h6? Is it necessary to add keywords to h3-h6?
Yes
And last question. What do you think about HTML structure? Do you place h1 on the top of the page, below h2-h6, and do not add, for example, h4 if there is no h3.
Headings follow a hierarchy, you can´t use an H3 without an H2 nor an H4 without an H3 or an H2.
One of their main purposes is to add a logical and linear flow to the idea/topic behind the content of a page.
Kind of like this...
The Search Engine Journal has a great article about this topic. There, they explain the following...
- H1 tags are used to denote the most important text, such as the main theme or title of the content.
- H2 and H3 tags are commonly used as subheadings.
- Finally, H4, H5, and H6 tags may be used to provide further structure within those subsections.
Full Article
Lastly, you need to understand the following, just because something is considered a ranking factor (like headings and subheadings) it doesn´t mean that by optimizing a page for those it will automatically take a page that is stuck on page 2 or 3 and place it in page 1 of Google.
It´s a ranking factor but it´s a
SMALL ranking factor.
But the fact that they are a small ranking factor doesn´t mean you will start to ignore them because, in the great scheme of things, the way you improve a site´s SEO health is by optimizing as many elements as possible on that page for has marginal as they might be.
Also, we need to optimize pages based NOT only on Google´s Webmaster Guidelines and on SEO best practices but also to enhance our visitor's user experience (UX) and, headings and subheadings provide that.