If there is a timing issue then the player with initiative decides, this means if a creature has 2 effects controlled by different players then the player with initiative decides what happens first.
Incorrect, imo.
A creature that regenerates ( owning player effect ) and that will take damage from an Idol ( opposing player effect ) can choose the order it which it resolves both effects. Normally Regenerate first, then take 1 damage.
The owner of the idol has no say in this, no matter who has initiative.
in the example of ghoul rot or death link vs regenerate, since the effects are controlled by different players, the player with initiative decides in what order they take place.
Again incorrect, imo.
A creature that regenerates ( owning player effect ) and that will take damage from a Ghoul Rot ( opposing player effect ) is the same example as above.
Death Link and Regenerate is different.
In the examples above we're always talking about
two effects on 1 creature.
In case of Death Link and Regenerate we're essentially talking about
1 effect on two creatures.
The controller of Death Link can heal and deal damage and the controller of the Regenerator can regenerate.
In this case it's the player with initiative who can resolve his effect first.
So, if the player that controls the Death Link has initiative it is possible to kill the creature before it gets a chance to regenerate.