Is there a correlation between the Earth's spin, the moon, and temperature? Based on NASA's arcticle, changes to land, ice sheet, ocean, and mantle flow affect Earth's spin.
Does the moon's elliptical orbit around Earth also affect Earth's spin? What effect does distance play?
The moon has also been drifting away continuously from the Earth. I've read that's due to the Earth's slowing axial rotation.
Would the moon's exodus from the Earth eventually reverse with Earth's recent trend of faster spining?
Would a faster spinning Earth increase the friction between the ocean and land, increasing the global temperature?
Does global warming perpetuate a cycle of faster rotation and and warmer oceans?
 A: 
Does the moon's elliptical orbit around Earth also affect Earth's spin? What effect does distance play?

The moon's orbit affect's earth's spin.  The eccentricity is not especially relevant, but the distance is.  The closer the moon, the stronger the tidal forces, and (to a first-order), the greater the coupling between the two.  That would suggest slowing is greater with a close moon than a distant moon.
But there's not a simple relationship between the two.  The coupling strength likely depends on specifics of earth's oceans.

Would the moon's exodus from the Earth eventually reverse with Earth's recent trend of faster spining?

No.  It is the fact that the earth's spin rate is faster than the moon that is causing both the general slowing of the earth's rotation and the recession of the moon.  Only when the two have the same rotational speed will the recession stop.

Would a faster spinning Earth increase the friction between the ocean and land, increasing the global temperature?

Might be a good question for earth science SE, but to a great extent, no.  The thermal energy released from tidal friction is not a significant contributor to the heat balance at the surface of the earth.

Does global warming perpetuate a cycle of faster rotation and and warmer oceans?

Global warming may well affect the earth's rotation rate in the short term, due to movement of mass (water) from the poles to the equator.  Over longer periods, the rebound of the crust makes the relationship much more complex.
But, the idea of a "faster" or "slower" earth over the last century or so is teeny on a percentage amount.  The change in the earth's speed likely has no practical effect on things like atmospheric and oceanic flows.  The rotation rate is roughly constant over millennia unless you can measure to the millisecond.  Other effects on the atmosphere dwarf these changes. I'm not aware of any evidence that rotational changes of that scale are important in the modeling of the atmosphere or climate.
A: This is a change that's happening over bullions of years. So the changes exist, but are so small they have little relevance on a timescale of years or centuries, probably not millennia either.
