They don't fall a gravity well, they follow straight lines in a curved spacetime. Not subject to the other forces everything follows the straightest line (geodesics) it possibly can in a curved spacetime.

The field equations define the spacetime geometry but they are very hard to solve, you will gain little insight from them. Instead you should try to understand the concept of a geodesic, how they are extremes of a variational problem, how they are calculated and the physical/geometrical intuition behind them.

A standard particle is not a point in 4D, it's a track, if it's locally static (compared to you for example) it's still churning happily along the t-dimension. In GR, the 4D spacetime is curved, so when you burn along the t-dimension locally, you might be seen as moving along one of the spacial dimensions as seen from afar (like, when you observe another guy falling down a building or observing dust getting swooped up by a black hole).