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The moon's mass is around 7.342 * 10^22 kilograms. As a civilization we are not capable of making any kind of a meaningful dent compared to that.

1. the article explains how many materials could potentially be sourced on the moon and provides potential magnet compositions to address that as well. 2. The moon weighs ~8.1 x 10^19 tons, if we use their iron based magnet design and ship everything from the earth (iron is present on the moon), it would require ~1 million tons aka 10^6 tons or approximately 0% of the weight of the moon. 3. See above.

I don't think we could conceivably launch enough mass onto the moon to meaningfully affect the tides.

For #1 this is addressed in the linked paper.

For #2 and 3, no. Such a construction project, even using entirely materials transferred from Earth, would not meaningfully affect the relative mass of the Earth and Moon.