You may stay for a maximum of 29 days in the U.S. on C-1 visa. You are required to leave the U.S. on the proposed flight or ship of departure, or within 29 days, whichever is earlier.
No, you may not extend your stay on C-1 visa. If you want to extend your stay you should apply for appropriate B-1/B-2 visas or can travel on Visa Waiver Program.
Note: If a foreign national seeks layover privileges for purposes other than for transit through the U.S. (for example, to visit friends or engage in sightseeing), he/she will have to qualify for the type of visa required for that purpose.