Question

is the distance between any two longitudes always the same.

Answer 1

the distance between two longitudes are not always equal . As we go near the poles , the distance between two longitudes decreases and distance between two longitudes is greater in the equator

Answer 2

if the two longitudes are in one degree apart , the distance along the parallel is always within 0.6 meter of "the great circle" distance ----but if the two longitudes are farther apart you can't avoid some complication ,if you are after "great circle " distance rather than distance along the parallel.