No, copying a spell does not count as casting it.
No, copying a spell in Magic: The Gathering does not count as casting it.
No, copying a spell is not considered casting it.
No, copying a spell is not considered casting it in Magic: The Gathering.
No, cycling does not count as casting a spell in the game.
No, mutating a creature does not count as casting a creature spell.
Yes, replicating a spell counts as casting it.
In Magic: The Gathering, you can copy a spell if you have a card or ability that allows you to do so. You must pay the spell's mana cost and follow any additional requirements specified by the copying effect. The copy will resolve separately from the original spell and will not count as casting the original spell.
Transfiguration is spell casting.
Mana empties from your pool immediately after you finish casting a spell.
No, playing a land is not considered casting a spell in the game of Magic: The Gathering.
Copied as in the past participle to reproduce something is the correct spelling so you were correct.
That is the correct spelling of "duplicating" (copying, repeating).