Yes, you may apply for Extension of Stay on H-1C visa. In general, all H-1C foreign nationals should be admitted for a period of three years, if otherwise eligible under statute and regulation. In the case you are admitted to the U.S. for a period of time less than three years, the facility may file Form I-129, Petition for Nonimmigrant Worker to extend your stay.
Note: The H-1C category is scheduled to expire on June 13, 2005, so all H-1C petitions must be filed by that date.
Yes, you may apply for Change of Status while on H-1C visa. If you are changing the job to H-1B or TN (incase if you have to move to non-disadvantaged areas), have your employer file Form I-129, Petition for Nonimmigrant Worker, at the USCIS Regional Service Center with jurisdiction over your case. Form I-539, Application to Extend or Change Nonimmigrant Status must be filed for dependent spouse or children by the employer.