Could we survive without our moon?

It all depends on whether you mean without the moon throughout Earth's history or hypothetically this instant.

As I understand it, the impact hypothesis is the most favoured story for creation of our moon. It sets forward that the Moon was likely formed by an impact between proto-Earth and a large, roughly Mars sized planet which threw off some matter which coalesced into the Moon we know now. It is hypothesised that this impactor may introduced additional iron into Earth's composition making the Earth's magnetic field possible which protects us from much of the solar wind. And it may have given Earth it's 23° axis.

The impact is also hypothesised to have introduced a large amount of angular momentum (spin) to the Earth. The Moon is spinning away from orbit very slowly as it takes this angular momentum away from Earth which has been good news for life on Earth historically as it may have slowed down the Earth's rotation from a 6 hour to 24 hour day so far giving more stability to the climate.
The influence of the moon's gravity has kept the earths rotational axis more stable over the last few billion years than that of other planets. This has diminished climatic variability at any given place on the earth. That relative stability must have contributed to the evolution of more complex organisms (humans) than may have been the case without the moon.

Had the earth's axis shifted substantially enough for the continent of Africa to move into a polar region prior to the evolution of homo sapiens, it's quite possible our primate ancestors would have gone extinct.

Now that we're here and suitably adapted to live in virtually every climactic region of the globe, we would likely survive the loss of our moon. Al Gore would sure freak out though.
Probably.

The severe diminution of ocean tides would certainly affect the food chain, but it wouldn't preclude our continued existence, just our maximum sustainable population.

Our long term climate would be less stable, but current thinking is that the instability would not be enough to wipe us out.

My life might be in jeopardy as the most popular answer I have on Quora, by a staggering margin, is about the Moon. I might have to kill myself.
Absolutely.  The moon is not essential for any of the processes that allow us to live the way we live.

That said, it is certainly possible that the moon has gotten in the way of asteroids that would have produced mayhem had it hit the Earth.  It's also possible that the added mass of the moon could have attracted asteroids towards us.  The moon really isn't that large and doesn't shield that much of the sky.  It's kind of like saying that putting a metal cigarette box in your pocket will prevent you from getting shot.

It's also possible that the moon's stabilizing effect on our planetary axis made it a bit easier for us to survive by moderating seasons.

We should survive, but condition will be worst.

If there will be no moon (at this moment I see three main points, there is much more)

  1. Night will be dark, because no Sun ligth reflected on its surface.
  2. Moon is a barrier for some of meteorites. They will hit on Earth
  3. Inflow/outflow are caused by Moon gravitation. Probably it will have big influence for climat

If an alien came to earth and was killed, would this be considered murder or would it be like hunting an animal?

The view of the American legal system is clear. Murder is the killing of another HUMAN in self-defense or under justifiable provocation. Here the victim is not a human. So there are no laws under which the shooter can be charged with murder. Still there are other aspects that need be examined:i) Alien is

How can one planet pull another planet?

Everything with mass also has a gravitational field. So the earth's gravitational field extends outward, limited only by the speed of light. So if you can see it in a telescope, gravity is pulling it toward you. That's what gravity does.F=G*m1*m2/(r*r)That's the equation for the force of gravity between two