Crickets (also known as “true crickets”), of the family Gryllidae, are insects related to bush crickets, and, more distantly, to grasshoppers.
The Gryllidae have mainly cylindrical bodies, round heads, and long antennae. Behind the head is a smooth, robust pronotum.
The abdomen ends in a pair of long cerci (spikes); females have a long, cylindrical ovipositor. The hind legs have enlarged femora (thighs), providing power for jumping.
The front wings are adapted as tough, leathery elytra (wing covers), and some crickets chirp by rubbing parts of these together.
The hind wings are membranous and folded when not in use for flight; many species, however, are flightless. (source)
So can hamsters eat live crickets?
Yes hamsters can eat crickets. As long as they are bred in captivity.