For me, when SEO is more important than branding, the company name goes at the end of the tag, and I use a variety of dividers to separate as no one way performs best. If you have a recognisable brand – then there is an argument for putting this at the front of titles – although Google often will change your title dynamically – sometimes putting your brand at the front of your snippet link title itself. I often leave out branding. There is no one size fits all approach as the strategy will depend on the type of page you are working with.
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.
Your SEO keywords are the keywords and phrases in your web content that make it possible for people to find your site via search engines. A website that is well optimized for search engines "speaks the same language" as its potential visitor base with keywords for SEO that help connect searchers to your site. Keywords are one of the main elements of SEO.
Yes, you need to build links to your site to acquire more PageRank, or Google ‘juice’ – or what we now call domain authority or trust. Google is a link-based search engine – it does not quite understand ‘good’ or ‘quality’ content – but it does understand ‘popular’ content. It can also usually identify poor, or THIN CONTENT – and it penalises your site for that – or – at least – it takes away the traffic you once had with an algorithm change. Google doesn’t like calling actions the take a ‘penalty’ – it doesn’t look good. They blame your ranking drops on their engineers getting better at identifying quality content or links, or the inverse – low-quality content and unnatural links. If they do take action your site for paid links – they call this a ‘Manual Action’ and you will get notified about it in Google Search Console if you sign up.
The SEO starter guide describes much of what your SEO will do for you. Although you don't need to know this guide well yourself if you're hiring a professional to do the work for you, it is useful to be familiar with these techniques, so that you can be aware if an SEO wants to use a technique that is not recommended or, worse, strongly discouraged.