Outmuscle

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.

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.

Because state-based actions don't destroy a creature with lethal damage marked on it until a player would receive priority, gaining indestructible from Outmuscle will save your creature if it's dealt lethal damage in the fight.

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.

If the creature you control is an illegal target as Outmuscle tries to resolve, no creature gets a +1/+1 counter. If that creature is a legal target but the creature you don't control isn't, it still gets a +1/+1 counter and gains indestructible if appropriate.

You can't cast Outmuscle unless you choose both a creature you control and a creature you don't control as targets.