This is irrelevant, you want to add oxygen into the wort to help the yeast feed.
Yes you do, but that shouldn't happen at the mash stage. You should be avoiding adding too much oxygen at the mash stage to avoid creating any oxidation, and any oxygen that is introduced during the mash will be driven off by the boil so won't be available to the yeast anyway. Once the wort is cooled and ready to go into the fermenter is the time to oxygenate for the benefit of the yeast, not before.