If reality isn't real and our dreams are, I'm pretty sure someone would have realized that by now, don't you think? To be completely honest, I don't think that our dreams being reality is a possibility, because we would have come quite close to death many times, and very frequently at that. Saying dreams were reality would be saying things such as that teleportation is possible, that one can see things in a third-person view, that one can come into and out of existence at times, etc. If you think about it this way, it makes perfect nonsense.
Of course, I at times ponder this as well; but the truth is that everything has a place in space and time, and everyone can see the same forms, shapes, and objects, though not the same colors and quality that others see. The only reason things may appear of a different color or quality is due to traits such as colorblindness and nearsightedness. You know this is true, for if it were false, one would not be able to talk with others about [example] a movie that aired in a theater a few nights ago. I'm not quite sure how to put this into better words.
As for that last question...nobody can truly know. For all that we know, we're just being controlled by a higher entity and think that we're free of will, or we might actually be free, or somewhere in between. To be honest, you're still living life and enjoying it, so why care if you really were being controlled or anything such? Even if this were true, it wouldn't matter if you knew or not, because you'd still be in that entity's control.
Nobody can prove or disprove the inexplicable, one can only find a stance they like best and attempt to uphold that stance; so it's really pointless to debate whether the Big Bang or God really happened.