Mel can definitely see the future, but interpreting what she sees is difficult. She may see Stannis, say, winning a battle, but there's no context in that to tell her what battle, when, so she fills in the blanks, often incorrectly. She definitely knew what she was doing with Renly, but beyond the ability to do that shadow attack, I don't think she can actually influence outside events, only see them. I would pay particular attention to the bathtub scene between Mel and Selyse in season 4 where she talks about tricks and how sometimes lies can lead to greater truths. That scene has probably the best insight the show's given so far into how Mel operates.
As for her God, I don't think you're ever going to get a clear answer one way or the other on whether or not any of the gods exist. There is definitely something supernatural in the world, but whether that's a god or whether it's just some magic force people can use, and then attribute the power to a god, I don't think we'll ever know for sure.
