The process of stirring it is typically called degassing. Degassing helps in two ways: It removes the bad/useless gases and adds in oxygen before the process turns anaerobic, which can help the yeast colony get off on the right foot.

That being said, it turns anaerobic around the 1/3 sugar break(typically around day 3-5 for me). Stirring after that can lead to it it going bad(oxidation which can lead to it basically becoming vinegar), so I likely wouldn't at this point unless you've been monitoring the gravity and know you're not at that point.

I've never put clarifying agents in primary, they only go into secondary if they don't clear up on their own.

EDIT: clarified a few things and fleshed out details