The moon is a useable source of energy, it's called tidal

At a far enough relative distance, the Earth and moon DO act as one large mass. You will have to be a little more specific with your second question. What specific means of energy farming from this system are you proposing if any?

Nothing acts as one large mass, not even the Earth or the moon individually. In Newtonian physics they're seen as masses at single points because at a certain distance that's close enough to what they act like and it makes the math easy, but nothing in reality actually acts like that. If you tied the Earth and moon together then nothing would change, they would act like they do now.

No, the gravity would not act as one large mass. Imagine a rope made from one thin strand of spider silk … there would no effect at all. However, from a large enough distance, the Earth-Moon system appears pretty much like one gravitational point. At about 100 times the Earth to moon distance.

The moon’s motion away from the Earth is not a constant rate. Every month, the moon gets closer by about 13,000 miles, then it gets further away by about 13,000 miles. On average, over many decades, the distance increases by about 1.5 inches per year.

But that 1.5 inches doesn’t matter for getting energy from the moon. The moon going around the Earth is what cause tides, and we can and do get energy from tides.

https://education.nationalgeographic.org/resource/tidal-energy

The earth rotates once every 24 hrs, whilst the moon takes about 28 days to make a full circle. Your rope would wrap around the earth until it snapped.

If you let the earth end just dangle freely, it would move a little slower than the rotational speed of the earth 465m/s (1040mph or Mach 1.5), and alternate between dragging along the ground and being hoisted up into space, as the Moon moved in its orbit from perigee to apogee

If this was feasible (it isn't), you could grab the cable when the Moon is at it's closest, then hold on and let it pull you into space. Timed right, you'd get a maximum altitude of 42,200km, which is enough to get to geostationary orbit and then some

The Moon and the Earth do act as one mass if you zoom out enough but every person has their own minuscule gravitational force as well. Even the ISS is attracting the earth toward it. Beyond that, that massive rope you’re using will have its own gravitational force that, if not created from resources on the moon or earth would introduce its own gravitational forces. As far as the energy you’d gain fro. The moon moving away from us, yes theoretically, you could harvest energy from it. At that point however, you’d already have build. System that re-orients the rope to the moons position relative to earth and if you have a track/system set up to accomplish that Herculean task (think The Line x a billion) you could just use that orbital motion to create as much energy as you need. It would be cheaper and probably more efficient to just build structures that harvest the current tidal energy the moon produces in the oceans. Hell, I’m sure you could build some giant canal and put a hydro-electric damn in the middle that creates power both ways. That would solve for your rising oceans problem a bit too. Alas, even these tiny versions of ideas are still multi-trillion dollar projects that no country, if not the entire worlds economy, could afford.

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The sun, the planets, moons and comets around each of the planets all act as one, as we move through the universe. Moon has tidal effects on planet earth. The Sun provides life, solar and invisible rays to planet earth.

would it show as two gravitational points with nill in the middle, interesting question?

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