What each record type does
A/AAAA records point a domain to its server's IPv4/IPv6 address. MX records say which mail servers handle email for the domain, in priority order. NS records name the authoritative nameservers for the domain. TXT records hold arbitrary text, commonly used for domain verification and email authentication (SPF, DKIM). CNAME aliases one hostname to another. SOA holds administrative details about the zone, including its serial number for tracking changes.
Why not every record type appears for every domain
Only record types that actually exist for the domain are shown - most domains won't have every type (a domain with no custom email, for instance, may have no MX records at all), so an empty result for a specific type usually just reflects that the domain simply doesn't use that kind of record, rather than indicating a lookup problem.
Why DNS changes don't appear instantly everywhere
A DNS change propagates based on the record's TTL (time to live) - the duration DNS resolvers are told to cache that record before checking again. A short TTL means changes show up quickly almost everywhere; a long TTL (common for stable records like NS) means some resolvers worldwide may still serve the old value for up to that TTL's duration, occasionally as long as 48 hours for very conservative settings.
What TXT records are typically used for today
Beyond simple domain ownership verification, TXT records are the mechanism behind SPF (specifying which servers are allowed to send email for a domain) and DKIM (a cryptographic signature proving an email wasn't tampered with) - both important for email deliverability and for making it harder for others to spoof your domain in phishing emails.