Is glutamate always involved in the deamination and amination of the other amino acids?
For most amino acids, the removal of the α-amino group involves α-ketoglutarate and glutamate. The amino group is first transferred to a-ketoglutarate by transaminases, and the resulting glutamate is then deaminated (via glutamate dehydrogenase) to yield ammonia. 


The same is true for amination. Glutamate and glutamine are the two major amino group-donors. Most ketoacids are converted to their respective amino acids by transamination involving glutamate or glutamine. Glutamine can be synthesized by amination of glutamate with ammonia without transamination (via a synthetase enzyme) and glutamate can be aminated with ammonia too.

Exceptions do exist, of course. For example, Not all transaminations involve glutamate/glutamine (as this user has replied), and serine and threonine can be directly deaminated (via dehydratase enzymes, as opposed to the dehydrogenase used for glutamate).