[1] Which half of the field is the leg side therefore depends on whether the on-strike batsman is right-handed or left-handed.
When the batsman steps backwards from his normal batting stance on the crease as the ball is bowled, he is said to be moving towards the leg side.
The names of fielding positions often include the words "leg" or "on", and they reflect this convention.
With a left-handed batsman, the leg side is analogous to the half that includes right field and first base.
Thus hitting to the leg side is directly visually analogous to "pull" hitting in baseball (though since all fair territory in baseball is forward of the batter, "on" would more exactly match this area of the field).