On a lathe X should always move to positive as the tool moves away from centre.
Even on a lathe with twin turrets, the controller should be smart enough to know what direction is positive depending on what tool/turret is selected, although I think there is a bug in Mach3 when running front and rear turrets.

G0 is just a rapid move.
G53 defines machine coordinates, but it's non-modal I.e. you have to put G53 in front of every coordinate to move to machine coordinates, other wise it will default to the active tool/offset coordinates. You would typically use a G53 for the tool change location move.