What are 'Company President' duties?

It's actually a legal and structural thing. When a company is incorporated, the company must name a point person that is the key legal point-of-contact for the company - that person is called the President. Hence the President of a corporation is a legal role filed with the state of incorporation.

The CEO is an executive role - and not a legally required one. While almost all companies have CEOs, it is theoretically possible not to have a CEO, or to have multiple CEOs.

The Chairman is the leader of the Board of Directors - again a corporate norm, but not legally required.