Well you clearly took a chunk of your time coming up with this! 
Got some questions on some things if you don't mind:
How would pet food & training work?
Does it just give a much bigger bonus compared to the 5% gain from the players regular gains?
How would active skills be used?
With the already 1-2-3-4-5-6 would these active skills move into Q-W-E-R.. ?
It could be very tedious having to push that many buttons in challenges.
Is everything in the PP Shop the same?
Is the pets Base Damage the same / per level & tier?
- I'd assume these two values would just be played with until it's balanced¿.
Some of these are questionable as they don't really work with iou.
Ex/ Stun (active skill), that could ONLY help in pet arena, disabling him for x turns.
I'd assume that would just have to increase the kill timer outside of pet arena? Would have to change the name of that if so.
I'm hesitant with how the 'pet levels' work, balancing that for all players would be a nightmare ¿. (The exp gain)
Still like it, but.. would likely need a lot of buffs/nerfs to things as it's a huge change requiring tons of values.

Got some questions on some things if you don't mind:
How would pet food & training work?
Does it just give a much bigger bonus compared to the 5% gain from the players regular gains?
How would active skills be used?
With the already 1-2-3-4-5-6 would these active skills move into Q-W-E-R.. ?
It could be very tedious having to push that many buttons in challenges.
Is everything in the PP Shop the same?
Is the pets Base Damage the same / per level & tier?
- I'd assume these two values would just be played with until it's balanced¿.
Some of these are questionable as they don't really work with iou.
Ex/ Stun (active skill), that could ONLY help in pet arena, disabling him for x turns.
I'd assume that would just have to increase the kill timer outside of pet arena? Would have to change the name of that if so.
I'm hesitant with how the 'pet levels' work, balancing that for all players would be a nightmare ¿. (The exp gain)
Still like it, but.. would likely need a lot of buffs/nerfs to things as it's a huge change requiring tons of values.