its confirmed in the movie that she is his daughter. remember the flashback of when the ship was taking off and she was screaming for it to come back? also she mentioned many times that she was "waiting for someone to come back". and yeah that does make sense, but if r2 knew they had the only missing piece of the map, he would have surely given it to them the moment he found out.
It's never actually confirmed in the movie that Rey is Luke's daughter. One could say it's hinted at plenty of times, like Maz telling Rey that what she is looking for is not in her past but her future. Even in the flashback when the ship is taking off and shes yelling at them to come back, you don't know who she is addressing that to. You do hear obi-wan speak to Rey as well, so that add some more interesting things to the mix. There are several possibilities as to who's daughter she could be (some people have suggested her being somehow an obi-wan descendant, or a solo), with Luke's being the most popular and seemingly evident thus far.
As for the R2 thing, who knows for sure, there are a lot of possibilities and reasons for how he came back to power. Will be easier once we find out more about Rey I guess.