A stack example, please help

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Could someone please explain how this stack would play out. The bottom spell/ability of the list is first played, the top spell/ability is last played. Please forgive my spelling.

Prodigal Pyromancer taps to deal 1 damage to Grizzly Bears
Cloud Shift to Prodigal Pyromancer 
Lightening Bolt to Prodigal Pyromancer
Prodigal Pyromancer taps to deal 1 damage to Grizzly Bears 

And what if it was a Vulshock Sorcerer instead of a Prodigal Pyromancer (i.e. has Haste)? 
Could someone please explain how this stack would play out. The bottom spell/ability of the list is first played, the top spell/ability is last played. Please forgive my spelling.

Prodigal Pyromancer taps to deal 1 damage to Grizzly Bears
Cloud Shift to Prodigal Pyromancer 
Lightening Bolt to Prodigal Pyromancer
Prodigal Pyromancer taps to deal 1 damage to Grizzly Bears 

And what if it was a Vulshock Sorcerer instead of a Prodigal Pyromancer (i.e. has Haste)? 



In order, these things happen:
First Pyromancer's ability resolves, dealing one damage to Bears.
Cloudshift resolves, Pyromancer is exiled and returns
Lightning Bolt fizzles and doesn nothing
Second Pyromancer's ability resolves, dealing one damage to Bears.

Haste doesn't matter for the resolution of anything.  It could use its abilty after the Cloudshift.

Also, normally you can't use Prodigal's ability twice in a row.  You would need to untap it first with Twiddle.  My answer assumes that you did.
 
Assuming I'm understanding correctly, what you've described isn't actually legal. The proper sequence of events would be:

1. Player 1 activates the ability of his or her Prodigal Pyromancer.
2. Player 2 casts Lightning Bolt targeting that Pyromancer.
3. Player 1 casts Cloudshift targeting the Pyromancer.
4. Cloudshift resolves, exiling the Pyromancer and then returning it to the battlefield. Despite the terminology, this is now a new Prodigal Pyromancer.
5. Player 1 would like to activate the new Pyromancer's ability, but it just entered the battlefield so its activated ability can't be activated.
6. Lightning Bolt tries to resolve, but its target no longer exists; it's countered by the rules and deals no damage to anything.
7. The ability put on the stack all the way back in (1) resolves, dealing 1 damage to the intended target.

If the Prodigal Pyromancer is replaced by Vulshok Sorcerer, then in (5) Player 1 does activate the ability. Then the rest of the sequence is

6. The newly activated ability resolves, dealing 1 damage to the intended target.
7. Lightning Bolt tries to resolve, but its target no longer exists; it's countered by the rules and deals no damage to anything.
8. The ability put on the stack all the way back in (1) resolves, dealing 1 damage to the intended target.

[edit]

If there are two distinct Pyromancer's in this scenario, or that you managed to untap the Pyromancer, then you want rudolf's answer.
Is there any way to stop the Pyromancer from dealing his point of damage?
 
Is there any way to stop the Pyromancer from dealing his point of damage?
 


You need something like Stifle to stop the ability.  Getting rid of the Pyromancer won't do that -- abilities on the stack exist independent of their source.
 
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