Into The Universe with Stephen Hawking – Questions

I was watching Into The Universe with Stephen Hawking on the Discovery Channel and I have a couple of questions.

First, this may seem simple, but how do engines work in space? If there’s nothing for the engine power to push against, how do they push things forward?

Second, on the show, they mentioned that everything in the universe appears red in tint because of a doppler something theory. Like a car going past you. While it’s coming towards you, it’s blue in tint, but when it passes and goes away, it becomes red in tint. But if you apply this to everything in the universe, all things would not be moving AWAY from us. In fact, since we’re all moving in the same direction, there should be more things that are NOT red than are. We are moving with other things, and when spinning around, we look at things “behind” us, which are actually moving towards us. So SOMETHING should have the blue tint unless everything came FROM us and is moving away from us. We are also spinning around the sun, so on one of the round trips, things would turn blue, since we start moving towards other things.

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