Overload doesn’t change when you can cast the spell.
Effects that cause you to pay more or less for a spell will cause you to pay that much more or less while casting it for its overload cost, too.
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.
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.
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.