Absorbancy: Give Earth Man a free action and choose a standard Attack power that an adjacent character can use. Until your next turn, he can use that power.

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.

With the Absorbancy special power, what is considered a standard attack power?
Any power that appears under 'Attack' on the Powers and Abilities card.

Does the target of Absorbancy need to possess the standard attack power?
No. Absorbancy only requires that the character can use the standard attack power. So if a character has a special power that says something like "Sun Boy can use Penetrating/Psychic Blast and Pulse Wave" then Earth Man can use Absorbancy to use either P/PB or PW since those are both standard attack powers that the target can use.

For No Place to Hide, Alien!, is a standard speed power identified in the same way? Would it be any power that appears under 'Speed' on the PAC?
Correct. And also like Absorbancy, possession is not required. If a character can use Hypersonic Speed, for example, via a special power, then it can't be given a power action to use that HSS.