do all diamondback bmx bikes have a serial number on them?
Almost all bikes have a serial number on them.
Exceptions might be

A home made bike
A small bespoke framebuilder (rare)
A repaired bike where the part that had the number was replaced
A stolen bike, where someone has ground-off the number to inhibit identification.

A serial number is not overly useful, since you know the brand, hopefully the manufacturer has a system, or has records still, and lets you look them up.  More on serials: What is the purpose of a serial number?