My H-1 expires by the end of October. If I apply for change of status to F-1 by then, can I legally stay in US pending decision?

You would be al to remain in the United States pending adjudication of your request to change status assuming the request is filed prior to the termination of your H-1B status. You could not begin your studies until the request is approved. There  is no grace period. You will begin accruing unlawful presence immediately upon denial of your request to change status. You need to depart the country ASAP under such circumstances. The answer is the same regardless of the nonimmigrant status you currently possess.