Domain authority is an important ranking phenomenon in Google. Nobody knows exactly how Google calculates, ranks and rates the popularity, reputation, intent or trust of a website, outside of Google, but when I write about domain authority I am generally thinking of sites that are popular, reputable and trusted e.g. are also cited by popular, reputable and trusted sites.

Hi Noya, all the info suggests that dwell time IS taken into account in search ranking, and we know that Google measures time on page and bounce rate in Analytics, too. Plus the search engine gets smarter all the time. With the machine learning component of RankBrain, we wouldn’t be surprised if Google can tell the difference between sites where visitors stick around, bounces where the visitor gets an answer immediately, and bounces where the visitor keeps searching.
Length of site domain registration; (I don’t see much benefit ON IT”S OWN even knowing “Valuable (legitimate) domains are often paid for several years in advance, while doorway (illegitimate) domains rarely are used for more than a year.”) – paying for a domain in advance just tells others you don’t want anyone else using this domain name, it is not much of an indication that you’re going to do something Google cares about).
If you have a commenting system (like Drupal, Joomla or WordPress) that allows for search engine friendly links (commonly called dofollow links) from your blog or site, you will probably, eventually be the target of lots of spam, be complicated in tiered link schemes and potentially fall foul of Google’s webmaster guidelines on using the attribute in certain situations.
Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.