The power is the same. The only differences are how sensitive your eyes are to those different wavelengths (green looks brighter mW for mW) and the wavelength absorption of your target (varies based on target color versus laser wavelength)
Not specifically. As FrothyChimp said, wavelength absorption plays a large part in this. For example, a blu-ray is able to light white matches at a much lower power than red or green.
You have, as countless others, mixed up visibility with optical power. The only reason 532nm appears brighter is because our retinas are more sensitive for that wavelength than 650nm. End of story.
Altough I don't blame you, because loads of companies sell green lasers on the internet. Many of them are unexperienced with lasers, and says stuff like "green laser - much more powerful than red laser." Because of this, many people believe that this is the case.