Not a dumb question at all. Interestingly enough, the moon is already slowing down the Earth's rotation, and it has been doing so for billions of years. Through tidal forces, the moon's orbit is gradually being raised at the expense of the Earth's rotation being gradually slowed. Right now, the same side of the moon always faces the Earth. In the far future, the same side of the Earth would always face the same side of the moon. The day would be much longer and the moon would be much farther away. However this would take about 50 billion years, which is a lot longer than the solar system has left in its current balance.

The amount of mass humans would extract from the moon through mining would not change this in any appreciable way because the moon is just too massive.

Short answer: the Moon is just huge. It's not conceivable that we do any significant change to the mass ratios.

I'm not a physicist, but I'd say the mass of the moon slows down the rotation of the earth, so moving the mass from the moon to the earth would make it spin faster (or at least, slow down less).

I'd expect it to speed to to conserve the angular momentum. Eg a figure skater pulling their arms in