What can be considered a backlink, and what not?

Jay Wessman said in his tutorials that Facebook shares, Twitter retweets and Pinterest repins are backlinks.

Others said that links on social networks are all nofollow, and it won't help website ranking.

Also, I heard many people saying that nofollow links from websites with high domain autority are a good sign for Google.

Who is right?
And I had another question: is commenting on blogs with no follow comments helping? What should I write in the "name" field, a common name or a partial match keyword related to my link?

Social Signals. Its not considered a backlink but its considered as a ranking factor.
As far as I know thats how it works

shaggy99 said:

Jay Wessman said in his tutorials that Facebook shares, Twitter retweets and Pinterest repins are backlinks.

Others said that links on social networks are all nofollow, and it won't help website ranking.

Also, I heard many people saying that nofollow links from websites with high domain autority are a good sign for Google.

Who is right?
And I had another question: is commenting on blogs with no follow comments helping? What should I write in the "name" field, a common name or a partial match keyword related to my link?

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Legitimate social signals will never hurt your site. Even if they don't give you a ranking boost, they have the possibility of giving your site traffic - either directly or through brand awareness.

N0follow links do have a purpose. It's debatable how much they help rank your site. I've found that they do help. Not as much as d0follow, but they help. They also help with the overall authority of your site. Am I going to spend a ton of $$ on a n0follow link? Probably not. But they're good to have.

Put your brand name or persona, whichever you're trying to build up, in the name field for blog comments.

It's literally a link that links back to your website. It's not rocket science