If an effect allows you to cast a spell without paying its mana cost, you can't choose to cast it and pay unless another rule or effect allows you to cast that spell for a cost. Similarly, you can't waive a cost reduction unless that effect says you may.

If one of the two target cards is an illegal target by the time Once and Future resolves, you'll put the other in the appropriate zone and exile Once and Future. If both targets are illegal, the spell won't resolve and you won't exile Once and Future.

If an instant or sorcery spell has an adamant ability, you perform the spell's instructions in order. You don't perform the adamant instruction before the spell resolves or before any other effects printed above it.

You choose which card will be returned to your hand and which will be put on top of your library as you choose those cards as targets, not as Once and Future resolves.

If you copy a spell that has an adamant ability, no mana was spent to cast the copy at all, so that ability won't apply.

Adamant effects check what mana was actually spent to cast a spell. If an effect allows you to spend mana “as though it were mana” of any color or type, that allows you to spend mana you couldn't otherwise spend, but it doesn't change what mana you spent to cast the spell.