I'm seeing that there are currently two things that trigger Morale Tests:

1. Friendly units engaged with a unit that is the target of a ranged attack make a severity one Moral Test.
2. When attacking the attacker may trigger a morale test of a severity equal to the number of panic icons on the dice plus however many of the defender's panic tokens the attacker would like to spend.

Is there any other time that a morale test is performed?

I believe from my reading of the Panic token rules in the Bane section of the RRG that the following statements are true:

1. Panic tokens may be spent to increase the severity of the morale test performed by a unit that is engaged with the defender of a ranged attack.
2. In an attack which there are no panic icons rolled on the dice, panic tokens may still be spent to force a moral test.

As of yet there are no other ways to trigger a morale test, but I suspect we will see more ways in the future.

To answer answer both of your other assertions, yes on both counts.