Yes, you may use Form I-129, Petition for a Nonimmigrant Worker, to apply for extension of stay. Extension may be authorized for a period of up to 30 months. Your total period of stay may not exceed five years.
Yes, you may engage in full time study on R-1 visa.
Yes, you may change employers on R-1 visa. The new organization seeking to employ you must file a new Form I-129, Petition for a Nonimmigrant worker, with the USCIS and have it approved.