Can Earth Man's ability, Opposing characters with the Cosmic keyword can't be given power actions to use standard Speed powers. Those characters modify their defense values by -2 when attacked by Earth Man, be used to stop standard powers given by way of special powers?

NO PLACE TO HIDE, ALIEN!: Opposing characters with the Cosmic keyword can't be given power actions to use standard Speed powers. Those characters modify their defense values by -2 when attacked by Earth Man.

if you're giving a character a non-free action to activate a standard speed power that needs a power action to activate, regardless of the source of the power, then Earth man's SP prevents them from doing so.

for example: a character with the cosmic keyword has a SP located in their attack. The power states you can use charge. because charge is normally a standard speed power that requires a power action to activate Earth Man would prevent the use of that charge, even though the charge was pulled from the attack stat.