Spells and abilities

I don't think that a blanket statement will cover this.  It really depends on the specific Squad and specific ability.

Lets say I have activated my Pummelroot Elementals.  I move all 3 of my Pummelroots, and all three of them are now in position to make an attack.  Action 3 is complete.  The first Pummelroot attacks and destroys the figure it attacked and has 1 additional damage to assign to an adjacent figure.  That damage is assigned before the second Pummelroot makes its attack.  So in that case, the ability is activated DURING the attack in action 4.

However, the Leyline Phantoms works differently.  As I move my first Phantom during action 3, I can walk through another creature.  My second one and third one may also use the ability.  Action 4 has not started.

But then there are the Restless Zombies.  Their ability does not even happen when they are activated as a squad, it happens when they are all in the graveyard and Liliana is activated to take a turn.

And then the Rhox Veterans.  Battle Formation does nothing when they are activated, rather is comes in to effect on the opponents turn.

Now a side-bar to both TRAMPLE and BATTLE FORMATION.  (I'm wondering if this may actually cover why the question came up).
A1_A2_A3
_B1_B2_B3
For Trample, imagine a row of three Pummelroots lined up single file with a row of Restless Zombies adjacent to it.
Suppose Pummelroot A2 attacks first, and chooses to attack Zombie B1.  On its roll it gets 4 and the Zombie rolls 0 meaning B1 is dead.  Pummelroot A1 no longer has an opponent to attack when it comes to its turn.  A better choice is to first attack with A1 against B1, because if B1 is defeated, A2 still might have an opportunity to attack.  However, if trample works, then Zombie B2 may also be dead.  So probably the best choice is to first have A3 attack B3.  That means that A2 will always be able to make an attack.  However, with lucky dice, all the zombies might be dead before A1 get a chance to attack a Zombie.

For Battle Formation, a similar effect can happen.  In the example, B2 gets +2 (for B1 and B3).  However, since B1 only gets +1 I would attack it first.  If I defeat it, then B2 is down to +1 .  If I also defeat it, then B3 gets no bonus.

There is a FAQ from Hasbro / WOTC that has this information in it.  This may be more what you're looking for.

Page 7 says, “You can only use activated abilities from the army card you chose.” Please, give a definitive list of the activated abilities currently in the game.

ARENA OF THE PLANESWALKERS
Gideon Jura, Combat Mage
-- Avatar of Justice - Static
-- Counter Strike - Triggered
Rhox Veterans
--Battle Formations - Static
--Trample - Triggered
Kor Soldiers
-- Detain - Triggered

Jace Beleren
-- Focused Thoughts - Activated
-- Mind Stealer - Triggered
Illusionary Projections
-- Collective Knowledge - Triggered
-- Illusionary Deception - Triggered
Leyline Phantoms
-- Phantom Walk - Static

Nissa Revane,
-- Keen Sight - Static
-- Sprint - Triggered
Elf Rangers
-- Squad Sprint - Triggered
Pummelroot Elementals
-- Trample - Triggered

Chandra Nalaar, Pyromancer
-- Double Attack - Triggered
-- Super Heated - Activated
Blazing Firecats
-- Haste - Triggered
-- Intense Strike - Triggered
Flamewing Phoenixes
-- Flying - Static
-- Rebirth - Triggered

Liliana Vess, Necromancer
-- Zombie - Static
-- Snuff Out - Activated
Restless Zombies
-- Darkness Arises - Triggered
Blighted Reavers
--Necrotic Stench - Static

Question 2)
2) When can activated abilities be used? (i.e., before moving the selected figure, in the middle of movement, after moving a figure but before attacking, between attacks, after attacking, etc.)

You can use activated abilities almost anytime: before moving, after moving and before attacking, after attacking. You cannot use activated abilities in the middle of a move or in the middle of combat.