Knowledge Pool

Artifact
Imprint -- When Knowledge Pool enters the battlefield, each player exiles the top three cards of his or her library.
Whenever a player casts a spell from his or her hand, that player exiles it. If the player does, he or she may cast another nonland card exiled with Knowledge Pool without paying that card's mana cost.
I would like to discuss some of the rules with Knowledge Pool as I am not sure I fully grasp how this card affects game states, though maybe I do and this can be helpful to others. I will start with this question and add more if needed.
I get the imprint ability, that makes sense, but what about after Knowledge Pool resolves and we have 6 cards “in the pool”
There are 2 more triggered abilities on this card:
The “exile spell” ability: “Whenever a player casts a spell from his or her hand, that player exiles it.”
And the “Play Free” ability: “If the player does, he or she may cast another nonland card exiled with Knowledge Pool without paying that card's mana cost.”
Now I understand that once I have resolved Knowledge Pool (Or tinkered into play) as the Active Player I will receive priority and can then cast the first spell “into the pool”.
From what I understand the "exile spell" triggered ability is triggered and put on the stack when I cast the spell, not when it resolves, and then the third ability triggers and is put onto the stack. Then if I don’t cast another spell, priority passes and my opponent can then do the same.
So what I am not fully clear on is this from the FAQ for Mirrodin Besieged:
If the original spell isn't exiled (perhaps because it's countered by another spell or ability before Knowledge Pool's second triggered ability resolves), the rest of the ability does nothing. The player doesn't get to cast an exiled card.
This makes it sound like any spell cast, can be countered before the second exile ability resolves, never triggering the third play free ability. But wouldn’t this “counterspell” be exiled with knowledge pool before it can resolve and need to be a counter spell cast from the pool?
For Example:
Knowledge Pool resolves.
Imprint ability resolves and Exiles: (Land, FOW, Jace2.0, Land , Nature’s Claim, Yawgmoth’s Will)
I get priority (since Imprint was not responded to) and then cast Mox Jet, opponent responds with Spell Pierce targeting Mox Jet.
Stack:
Mox Jet
Exile Jet
Spell Pierce targeting Mox Jet
Exile Spell Pierce
Wouldn’t the Exile Spell Pierce ability resolve first not allowing Spell Pierce to resolve and counter Mox Jet? Or does the exiling happen after the casting of the spell prior to priority passing? If so how could you counter the Mox Jet if it’s not on the stack to counter?
If that is correct they must be talking about, the exile ability resolving triggering the third “play for free” ability. So it would look like this:
Mox Jet
Exile Jet
Spell Pierce targeting Mox Jet
Exile Spell Pierce
Exile Spell Pierce Resolves, triggers “play free ability”, exiles Spell Pierce from stack into the pool.
Stack now:
Mox Jet
Exile Jet
“play free” Opponent chooses FOW targeting Mox Jet
FOW resolves countering Mox Jet and removing from stack to my graveyard since it is not exiled by knowledge pool) and Exile Jet has an illegal target and I don’t trigger the third play free ability.
Is that the correct way it works?
If it does work that way then am I correct that I could then counter the FOW with the Spell Pierce used to cast FOW from the Pool?Here is that example (after Spell Pierce used to cast FOW from Pool):
Stack:
Mox Jet
Exile Jet
FOW targeting Mox Jet (played from pool by Spell Pierce getting exiled)
Pool is now (Land, Jace2.0, Land , Nature’s Claim, Yawgmoth’s Will, Spell Pierce)
I then respond to the casting of FOW from the pool by my opponent and by casting my own instant (let’s say steel sabotage targeting an opponent’s tapped Mox Pearl) Can I then counter the FOW? Stack would look like this:
Mox Jet
Exile Jet
FOW targeting Mox Jet (played from pool by Spell Pierce getting exiled)
Steel Sabotage targeting Mox Pearl
Exile Steel Sabotage
Exile Steel Sabotage resolves, Steel sabotage is exiled into pool, and then I chose to cast Spell Pierce targeting FOW.
Mox Jet
Exile Jet
FOW targeting Mox Jet (played from pool by Spell Pierce getting exiled)
Spell Pierce targeting FOW
Spell Pierce resolves countering FOW and moving into the original owner’s graveyard, and leaves:
Mox Jet
Exile Jet
Exile Mox Jet resolves, removing it from the stack to the pool, and triggering the third play free ability.
Play free ability targeting Jace2.0
I end up all of this with a Jace 2.0 and a pool with (Land, Land, Nature’s Claim, Yawgmoth’s Will, Steel Sabotage, and Mox Jet)
Do I understand this correctly?