Does the enemy mourn its "fallen" to the same degree and reverence we do for our own?

Depends on the enemy. The current enemy is more a death cult than a military. They are happy to die as long as they kill some of us. That is not worthy of mourning. They don't mourn their own because they believe they have "martyred" themselves to the cause. It would be inappropriate for them to mourn their own. It is rather sick.