See whether a zone is signed, whether the parent publishes a matching DS record, and whether a validating resolver actually accepts the chain, which is the part the records alone cannot tell you.
DNSSEC proves your DNS answers were not tampered with. It says nothing about whether the mail leaving your domain is authenticated, and that is the check receiving servers actually run.
A set of DNS records that cryptographically sign your zone, so a resolver can prove the answer it received is the answer you published and not something injected along the way.
It is optional and most domains do not use it. It does not affect email deliverability and its absence is not a security failure. It matters most where a forged DNS answer would be valuable to somebody.
The DNSKEY is in your zone and signs your records. The DS is at your parent, usually held by your registrar, and vouches for that key. The chain only holds when both exist and match.
Almost always a mismatch between the DS at the registrar and the current DNSKEY, left behind by a key rollover or a change of DNS provider. The records look fine individually and the chain is broken.
No. It proves answers are authentic; it does not hide them. Encrypting the query itself is what DNS over HTTPS and DNS over TLS do, and they are unrelated.