G007 Juggernaut:

Movement:
This character can move through Blocking terrain. Immediately after movement resolves, destroy all Blocking terrain moved through. This character can move through squares adjacent to or occupied by opposing characters without stopping, and automatically breaks away, even if adjacent to a character than can use Plasticity.

My Mutant Brothers and Sisters:
Once per turn when an effect other than clearing removes an action token from Juggernaut, after resolutions heal him 1 click.

Mass Destruction:
Super Strength. When Juggernaut is given a MOVE action, after resolutions destroy all adjacent pieces of blocking terrain, then he can use Quake at no cost.

City-Wide Rampage:
If Juggernaut destroyed 3 or more pieces of blocking terrain during one of his actions, after resolutions remove an action token from him.

Shielded by My Helmet:
Colossal Stamina, Invincible. Juggernaut has PROTECTED: Incapacitate, Mind Control, Outwit, Pulse Wave.

Core Rulebook (Ver. 2018.01):

COSTED ACTIONS Page 7:
By default, four of the action types listed above (MOVE,
CLOSE, RANGE, and POWER) are costed actions and follow
these rules:
• Just before the action resolves, give the character
an action token. This signifies that you have
resolved the action.

Terrain: Page 19
Blocking terrain is the squares inside brown boundary lines. Heavy black lines running along the grid of the map are walls. Walls are blocking terrain along a line that occurs between squares instead of
filling them.

Questions:

1.)Does Juggernaut has to destroy adjacent pieces of blocking terrain to use Quake at no cost ? Or can he use use Quake at no cost after a MOVE action resolves ?

Scenario 1:
Juggernaut has no action tokens and is given a Charge Power action:

Question:

2.)Can Juggernaut remove an action token after using Charge, if he destroyed 3 walls during his charge move resulting in him not having an action assigned to him at the end of his turn ?

Scenario 2:
Juggernaut has been dealt 2 clicks of damage, has no action tokens. Then uses Mass Destruction Trait and destroys 3 adjacent walls after being given a MOVE action.

Question:

3.)Could Juggernaut be given an action token, just before the action resolves. Then remove the action token after using MOVE Action, if he destroyed 3 walls resulting in him being healed 1 click and not having an action token assigned to him at the end of his turn ?

Juggernaut can use Quake regardless of whether any blocking terrain is destroyed or not.

Juggernaut will have still been given an action, the token just gets removed.

Yes.

This part jumped out at me:

I see (and correct) this a lot:

Action tokens are placed at the resolution of an action - not the turn. There are tons of elements in the game today that are affected by this.

You may know it and just wrote it incorrectly but in case someone else reads through, how it works is:

Juggernaut does his thing and destroys 3 pieces of blocking terrain.

He makes a CLOSE (as free if it is Quake, or Object Attack, or just an attack).

Damage / knockback is determined.

Now Juggernaut receives his action token.

Then due to his trait (and destroying 3 squares of blocking) he removes an action token.

Then, if possible, he heals 1 since he removed an action token in a way other than clearing action tokens.

Why it matters game-wise is because if Juggernaut has 2 action tokens, he either cannot be given an action OR has to use Colossal Stamina to be given a costed action.

IF it worked where you just don't give an action token then he could just attack with 2 tokens on him and clear them at the end of the turn since he wasn't given an action token this turn.