Many registrars hide the owner's personal data by default under privacy requirements. An empty field does not mean the domain is free – the registration status is shown by separate fields in the report.
Not necessarily one physical server, but one network access point. A single IP on shared hosting can host many different domains at once – that is normal and does not link their owners together.
Possible reasons: a local block by the provider or a cached DNS entry, regional restrictions on the site's side, or a temporary outage that was already fixed by the time someone else checked.
It depends on the record's TTL and caching by intermediate servers – usually from a few minutes up to 24–48 hours for a full update across every provider.
Checks related to a domain name and a site's server: who owns the domain, what IP it is hosted on, whether the site works right now and which domains share the same hosting.
WHOIS shows who registered a domain and when. DNS records show where a domain currently points – to which mail server, to which IP address. The IP address itself is the entry point to the server where the site is physically hosted. A mismatch between what WHOIS shows and where the DNS records actually lead is a common sign of an unfinished move to a new host.
Before buying a domain, WHOIS is checked to find out whether it is free and who the current owner is. When moving to a new host, DNS records and the IP address are checked to make sure the domain points where it should. When users complain that "the site won't open", availability and the response code are checked first, not DNS – those are not the same thing.
SSL certificate and load speed checks are covered in the Technical SEO & Security section – they relate more to a site's technical state than to the domain as such.