Is it possible that Mercury collided with Earth, thus creating the Moon? I recently heard a theory that Mercury might have been bigger before a massive collision that shrunk it and sent it on its current orbit. I also heard that a possible explanation for the formation of the Moon is a collision between Earth and a Mars-sized planet. Also, there seem to be similar elements on both Mercury and Earth. Is there any line of research that investigates this possibility or is it immediately dismissable for various reasons? 
 A: The latter idea you talk about is the Giant Impact Hypothesis. It turns out that you can make a moon in a few easy steps (given the correct conditions):


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*Have a bunch of protoplanets whiz about on semi-chaotic trajectories.

*Smack two of them together at a 45° angle.

*Let the bits of the protoplanets that don't merge together be ejected from the resulting planet, with some remaining captured in orbit.

*Have this remaining matter form a moon.


Some notable features of the Giant Impact Hypothesis are:


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*The cores of both protoplanets stay together; only outer material is ejected.

*Much of the material stays in the system and does not escape.

*The two bodies are greatly changed by the impact. In other words, it's not like one simply gave a bunch of itself to the other.


Imagine that a more massive Mercury, in the early stages of the Solar System's formation, collides with Earth. In order for some of it to survive the impact, it must approach at a rather indirect angle. If it hits at 45°, 60° or some other large angle, it's unlikely that any of it will survive. It has to hit in a glancing blow. This is quite possible.
The resultant orbit would have a relatively high eccentricity, which would be whittled down over the years, courtesy of tidal forces. Mercury does have a famously high orbital eccentricity, though of course that doesn't imply that it underwent this sort of collision.
Most of Mercury would be stripped away, leaving an object with a large core. This is the case with Mercury today. However, this can easily be plausibly explained by having a smaller planetesimal hit it (e.g. Benz et al. (1987); you also mentioned it). This could be interpreted as a collision between Mercury and Earth, though.

Also, there seem to be similar elements on both Mercury and Earth.

Both have a decent amount of silicates, with Mercury having a higher percentage than Earth; the same is true for oxygen. However, Mercury has a high iron content. This is most likely because its core is large relative to the rest of the planet and is iron-rich. The general impact hypothesis explains this.
These could all be used in favor of your idea. But Wikipedia gives one damning observation:

MESSENGER has found higher-than-expected potassium and sulfur levels on the surface, suggesting that the giant impact hypothesis and vaporization of the crust and mantle did not occur because potassium and sulfur would have been driven off by the extreme heat of these events. The findings would seem to favor the third hypothesis [in which Mercury formed from the solar nebula]; however, further analysis of the data is needed.

So that's a large problem.
Here, by the way, it appears that "giant impact hypothesis" refers to a collision between Mercury and another protoplanet or planetesimal early on in its life; however, reasons suggesting such an event did not happen can also be applied to suggest that there was no collision with Earth.
