If you lose your balance during the swing then you probably made a bad swing, make sure your body is balanced on your front side at the end of each swing
The width of your legs in your set up is important because it allows for the legs to function properly so that your right thigh can catch up to your left thigh creating the correct downswing and allowing for increased power
In a one plane swing your arms are closer to your body and swing across your chest; in a two plane swing has the arms swinging up and down