Yes.
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Can I shoot into melee to stress my own unit?
Yes.
Can I stress during an activation if I know that the stress from said activation will put me over the threshold?
Yes, if you are under your MOR value.
Can a unit with an activation token and as much stress as its MOR, be the target of abilities that allow it to perform additional actions or activations? (Such as Alborc's "The Warg and the Crow")
To be the target of such effects, the unit needs to be able to perform the specified action or activation.
In the case of actions (that are not activations), only the requirements of the action will be checked (such as, not being engaged in combat to perform a ranged attack), and if those are met then the unit will be able to perform the action.
In the case of activations, given that a unit with an activation token and as much stress as its MOR can only activate to rest, if the effect requires the unit to perform any other action, then it won't be able to activate.
A unit with MOR 1 that already has an activation token activates again (receiving an stress token). Is this unit forced to perform a Rest action, given that it has an activation token and as much stress as its MOR?
No, the limitation of only being able to perform rest actions is checked before activating. A unit with an activation token and as much stress as its MOR can only be activated to perform the rest action.
A unit with an activation token and as much stress as its MOR can only activate to rest. In case that unit has a way to reduce its stress at the beginning of its activation, can it perform an action other than rest?
No, even if the unit's status changes, that unit could only activate to rest, no other actions can be performed.
If a unit fails the WP test to avoid being demoralized, does it also remove the stress exceding its MOR value?
Yes, no matter the result of the WP test to avoit being demorlized, the unit reduces its stress until it matches its MOR value.