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List the mail servers that receive email for a domain, in priority order, and see which mailbox provider runs them.
MX records only decide where incoming mail is delivered. Whether your outgoing mail is trusted depends on SPF, DKIM and DMARC. That's why a domain can receive mail perfectly and still have its messages flagged as spam, or be spoofed by anyone.
Lower numbers are tried first. Servers with the same number share the load. Higher numbers act as backups when the primary servers don't answer.
A single MX record pointing to '.' with priority 0 (RFC 7505). It announces that the domain deliberately accepts no email, which is good practice for domains that never receive mail.
Not directly; MX records control receiving. But a domain that can't receive mail looks suspicious to some filters, and without working MX you also can't receive DMARC reports sent to that domain.