Does gravity change with latitude and longitude?

Answer 1

Yes, but ..... not enough to notice. You need REALLY precise instruments to measure it.

But if transportation was absolutely free, you could make a nice bit of change buying several tons of gold at the top of a mountain (farther from the center of the Earth, therefore, slightly lower gravity) and selling it in Death Valley (closer to the center of the Earth, therefore higher gravity).

There are also "mass concentrations" in the Earth where local gravity is slightly higher than normal - again, by some tiny fraction of a percent. But it's enough so that NASA occasionally has to make tiny adjustments in the orbits of spacecraft to account for the uneven mass distribution around the world.