What Google thinks about Sub domain?

Subdomains are seen by search engines as different sites.

Sub domains are regarded as different site.
But the main site will have some effect on them and also the
sub domains will have some effect on main site.
So don't use subdomain if you are doing anything wrong else it is ok to use subdomain.

You will get more SEO from a domain name with keywords than a subdomain with keywords. So, you are handicapping yourself a bit there.

Not a big deal if you can't get the domain you want anyway.

Generally Google considered sub domains as an individual site only, but it is better if you try to avoid using sub domain as much as possible. Though a main site has some effects on sub domains that can help the sub domain site rank faster, but sub domain site also has an effect on the main website and affects its ranking or reputation.

Am I right in thinking that if you are in the niche of "Sleep Apnea" but the domain "sleepapnea.com" was taken, you could register a domain of "xyz.com" and then use a sub domain of "sleepapnea.xyz.com" and, with all other things being eaqual, you could achieve the same page ranking as "sleepapnea.com".

Google ranks pages, not domains. So it doesn't matter what is in the url bar be it,

siteurl.com/keyword
or
keyword.siterurl.com

Google will see them both as separate pages, with the keyword in the url.

BUT a sub domain url will not flow pr the same as a domain with a sub folder.

This page is full of contradictory and misleading information.
First, domain, sub-domain or sub-folders don't pass PR, link juice or whatnot. Only do-follow links and 301 redirects can pass link juice and PR. So you can have a sub-domain and link to it from the domain. This will pass PR. On the other hand, you can create a page from the main domain and not link to it at all, thus creating a dangling or orphan page that will never get PR or even be found by search engines.

Secondly, sleepapnea.xyz.com is not the same as sleepapnea.com or xyz.com/sleepapnea.php. Google places a lot of emphasis on keywords in the domain name but not so much on keywords in the subdomain or folder. Otherwise you will see a lot of these sites with keywords in the sub-domain or folder ranking on the first page. If you do a search for seo, you get seo.com on the first page. you don't see seo.xyz.com. The same applies to other competitive keywords in the serps.

Finally and most importantly, subdomains leeches off the trust from the domain, as mentioned earlier on. This trust is different from PR. There are some exceptions, for e.g. wordpress and blogspot subdomains pass on no trust. This is still an area with uncertainties as even robots struggle to differentiate between sub-domains and domains that should pass on trust.

I have one example I can cite. I created 2 new blogspot blogs at the same time. One was redirected to its own brand new domain abc.co.uk and the other to a brand new sub-domain created off a 5 months old domain 123.co.uk. Similar number of articles were published on each site and at similar intervals except brand new domain abc.co.uk had a few more backlinks thrown at it. However the subdomain blog was indexed as soon as a post was published whereas the other one still has to wait a few days, despite having a few more quality links. The subdomain blog has only 2 such links and is not even linked to the main domain; in fact it links to it, not the other way round.

If you use subdomains for your auto blogs, make sure atleast 3 to 5 posts with unique content. then only your site will get indexed clearly in google results.