Yes

You can use faster DDR3 in a slower system. You might have to use the CAS settings for the slower memory, but you can play around with these. You don't have to worry about the slower speed of the motherboard, the memory can always be run at lower rates.

Yes, the motherboard will clock it down to 1066/1333 unless you overclock it, at which point it tries to run at whatever you set it to.

A larger power supply is not more efficient than a smaller one. Power supplies have specific efficiency ratings, which are unrelated to their capacity.