Yes.
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If my Character joins a unit that has not activated during the round and we get to the “No one gets left behind” step, can they move since the Character removes their activation token when joining?
Yes.
What happens if a Character with a ranged attack bonus on the joined profile joins a unit without a ranged attack?
Since the unit itself cannot perform a ranged attack, that bonus is not applied.
A Character who joined a unit is considered a unit inside a unit?
No. A Character who joined a unit, be it Support or Officer, is considered a member of the unit and not an independent unit.
A Support Character inside a unit has a bonus skill that affects a target within X strides. Do we measure from the Character or the leader?
The Character is inside a unit, so all measurements must be made from the leader of said unit.
If a unit with a character joined suffers enough damage to lose all of its troops (except the Character) during combat, how should the Character unit be considered? Is it a new unit engaged in combat?
Even if effects of destroyed unit are resolved, the Character unit will be considered the same unit that participated in the combat (no effects such as "when you engage with a unit" will be applied).
When a Character leaves a unit, does the unit also receive an activation token?
No.
Can a Character leaving their unit move through friendly troops that are part of the unit they are leaving?
Yes (see errata. Move)
If a joined character leaves a unit and doesn't move, the new troop leader cannot be placed on its position, what should be done?
Since the troop leader cannot be placed it will remain in its current position, if this breaks the unit formation, next time it activates it will need to perform a move action to recover formation.