I take it the moon is heavier: on the side closest to the earth:...?
That is marginally true, I think, but it is not the reason why the moon always faces the same side towards Earth. If anything, it is a
consequence of that.
but why hasnt it been started rotating by asteroid collision?
You'd need a very large asteroid to significantly affect the rotation. And any rotation that started would gradually be damped out again.
shouldnt the moon rotate?
It does! It rotates about its axis about once a month - the same amount of time it takes to revolve once around the Earth.
The reason for this is that the Earth creates tides on the Moon (tides of land, not water, and not as large as the water tides we see on Earth). These tides tend to slow the Moon's rotation until it is synchronised with its revolution around the Earth.
The moon does rotate, just not on it's axis.
It does rotate on its axis (relative to the distant stars) - once every month.
To my knowledge (obviously feel free to surf the internet to check on it), the reason that it doesn't spin on it's axis is because of it's size. Since it's small it's cooled relatively quickly compared to the earth, this means that it's core isn't as molten as the earth, therefore gravity is effecting a mostly solid mass rather than a solid crust and molten core. I guess you could say the earth spins because it has both a moon and magma flow.
This is wrong. The Moon originally would have rotated faster, but tidal forces have caused its rotation to slow and become locked with its revolution around the Earth. Mars, like the Moon, probably doesn't have a molten core, but it rotates just like the Earth. Rotation has nothing to do with magma flow.
Ophiolite, In honesty if you were to model it's spin it wouldn't be on it's axis, it's spin would actually be on the earth's axis at least from 3D modelling.
In astronomy, spin on its axis is called "rotation". Orbiting around another object is called "revolution". The moon both rotates and revolves around the Earth.
I think it rotates with the Earth because it came from the Earth. If it was a separate body captured by Earth's gravity, it would have it's own rotational speed, independent of our's.
For a while, but tidal locking would still apply over time.