In Rebirth, will there be achievements like the original Isaac? If so, how much more power do you have in using the achievement system in Steam? Will the same achievements be coming back (but fixed) or will we be getting completely new ones, or a mix?

id say about 50% of the told achievements and unlocks will return. tons of new ones and tons of old ones will be flipped around and changed up. 

you have total power to do whatever you want achievement wise on steam, unlimited achievements!