Pressure. We sometimes will tie elastics differently (with a twist or figure 8 for example) to create greater pressure and thus force on a given tooth/bracket when we need to achieve greater movement on a given tooth.
Don't. Unless instructed specifically to do so. Twisting the elastics shortens them, increasing force. Elastics are designed to provide light continuous force, to which your body responds favorably. Increasing force, creating heavy force, can overcome your bodies ability to respond, actually slowing treatment. Follow your Orthodontist's advice to the letter for best results.
Nothing. They have the same strength either way, If the twist is only once or twice. Sometimes twisting helps the to stay on better. Dr Malerman is right on! .