Ok, I assumed the Silence were the ones controlling the TARDIS and we'll be learning more about how that works later on in the next half of the series. As for River being part TimeLord - we don't know how that works yet. The best explaination given in the episode was the Doctor guessing that it was to do with Amy and Rory traveling in the TARDIS. Remember when he tells the Silurian about his adventures with Amy and Rory from series 5 and how he had to reset the universe and then came back for them both on their wedding day. Now we know that the traveled with the Doctor the night of their wedding which means that Amy must have become pregnant in the TARDIS - remember that in one of the episodes, I can't remember which exactly now not that it matters, of this series where it is mentioned that Amy and Rory have a room in the TARDIS where they sleep and it was loosely insinuated that that wasn't all they got up to in that room.