I seem to have different views concerning these two.
I know Panharmonicon triggers "Enter the Battlefield" effects of artifacts and creatures you play after it so that's fine.
But since the card text states that if an artifact or creature entering the battlefield would trigger another existing permanent's trigger if that is what would normally trigger it, then would Animar, Soul of Elements get 2 counters instead of 1?
Since he is triggered by a creature being cast would it work? or would it only work if the text of the card would read: "Whenever a creature enters the battlefield, do X"
No, these two don't interact for the reason you mentioned: Animar triggers "on cast" which means that trigger occurs, and resolves, before the creature that triggered it enters the battlefield. Since the trigger happens before the creature enters the battlefield (while it is still on the stack), Panharmicon won't see it to cause it to trigger twice.
Your last comment is correct. Panharmicon would only double the trigger if the trigger said "whenever a creature (or artifact or "this object") enters the battlefield...".
I know Panharmonicon triggers "Enter the Battlefield" effects of artifacts and creatures you play after it so that's fine.
But since the card text states that if an artifact or creature entering the battlefield would trigger another existing permanent's trigger if that is what would normally trigger it, then would Animar, Soul of Elements get 2 counters instead of 1?
Since he is triggered by a creature being cast would it work? or would it only work if the text of the card would read: "Whenever a creature enters the battlefield, do X"
Your last comment is correct. Panharmicon would only double the trigger if the trigger said "whenever a creature (or artifact or "this object") enters the battlefield...".