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River came no where CLOSE to killing them all. There were probably millions of Silence all over the world. Remember, that had been there since "The fire and the wheel". That's a ding-dong long time. And when they issued the "You should kill us on sight", they subliminally directed all humans to kill them. However, since Amy saw one of the Silence before they went back to 1969 and tricked the Silence into issuing the order, the order had never been given, and thus, Amy saw one.
I think that is more likely to be the case, because she didn't kill the Silent when she saw it. Technically speaking, she would have seen the Moon landing and killed the Silent that very moment, without realizing what she'd done, but the other would have reacted to her attempting to kill a Silent.
So, it must be that that Silent was there because the Doctor and his companions had not gone back to issue the order.

Of course the Doctor planned his death. That's why he recruited Amy, Rory, River, Canton Everett Delaware III's older self, and the Doctor's own younger self. He was trying to get them to go back in time. He arranged for the boat to be there, of course, since he knew he would die and, like River said, entire empired would rip our world apart for just one cell of his body, since he was a Time Lord.
He then got shot by the Astronaut, which I believe was also in on it, to prove a point. Why he didn't just take them is beyond me, I have a feeling this is going to be something important to this season, not just those two episodes.
I'm also fairly certain in the course of this season history will be rewritten and the Doctor won't die. I'm pretty sure they'll RETCON that out like they do a lot of other things.

That's just my two cents.