There are four objects you will use constantly: user mailboxes, shared mailboxes (no licence needed under 50 GB, accessed by permission), distribution lists (one-way delivery to a group), and Microsoft 365 Groups (a mailbox plus a SharePoint site plus a Team). Picking the wrong object is the most common small-business email design error — 'info@' should be a shared mailbox, not a licensed user whose password is in a spreadsheet.
Mail flow depends on the Domain Name System (DNS (Domain Name System)). The Mail Exchanger (MX (Mail Exchange record)) record says where mail is delivered. Sender Policy Framework (SPF (Sender Policy Framework)) lists who may send as your domain. DomainKeys Identified Mail (DKIM (DomainKeys Identified Mail)) signs your mail. Domain-based Message Authentication, Reporting and Conformance (DMARC) tells receivers what to do when SPF and DKIM fail. Missing these is why a small business's newsletters land in spam and why their domain gets spoofed in invoice fraud.
For a delivery complaint, use message trace. It answers 'did it arrive, was it quarantined, was it rejected, or did it never exist' in under a minute, which is the difference between a professional answer and a shrug.
Shared mailbox access has three flavours: Full Access (read the mailbox), Send As (mail appears from the mailbox), and Send on Behalf (mail shows 'on behalf of'). Granting Full Access without Send As produces the classic 'I can read it but my replies come from me' ticket.