To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as an overload cost), add any cost increases, then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was.
If you don't pay the overload cost of a spell with overload, that spell will have a single target. If you pay the overload cost, the spell won't have any targets.
If you are instructed to cast a spell with overload "without paying its mana cost," you can't choose to pay its overload cost instead.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Christopher Moeller
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Because a spell with overload doesn't target when its overload cost is paid, it may affect permanents with hexproof or with protection from the appropriate color.
The controller of a creature that attacks if able still chooses which player or planeswalker it attacks.
If you cast Chemister's Trick with overload, only creatures you don't control that are on the battlefield when Chemister's Trick resolves are affected. Creatures that come under another player's control later in the turn are not.
If, during a player's declare attacker's step, a creature is tapped, is affected by a spell or ability that says it can't attack, or hasn't been under that player's control continuously since the turn began (and doesn't have haste), then it doesn't attack. If there's a cost associated with having a creature attack, the player isn't forced to pay that cost, so it doesn't have to attack in that case either.
