Why are you asking here?
Anyways its in what you asked:
"The earth's moon is thought to have formed when a Mars-sized planet collided with Earth during its final stages of planetary accretion."
This is because, in my science class at least, our teacher taught us that a Mars sized object collided with earth, and the debris from this caused the moon to form. This is also highly likely in early solar systems, as they are very dangerous with many objects crashing and colliding with other objects.
"Without the earth's moon, life on Earth would not be possible."
Maybe? I don't know. I think False on this one because we don't yet know how life came into existence, where compounds turned into organic compounds or something like that.
"The earth's moon is the smallest moon relative to its host planet."
I think that's Mars's moons, so false(Don't know much about astronomy)
"The earth's moon is the same size as the earth."
Very, Very, VERY unlikely. This would cause both the Earth and the Moon to rip each other to shreds with their own gravity, and we would have serious planet sized-problems.
Hope this helps!