How do I determine whether to change Centering Spring Strength in the Specific Game Settings window or in the Global Device Settings window?

Changes made in the Global Device Settings Window affect all profiles. Changes in the Specific Game Settings window only affect the Profile that is active when you make the change.

What effect does the position of the slider have?

The 0% position effectively eliminates force feedback sensations. The 100% position provides exactly the strength of force designed in by the game developer. Setting the slider at less than 100% scales the forces down proportionately. Positions over 100% increase low-level forces proportionately.