Yes, you may apply for L-1 visa extension using Form I-129, and L Supplement. Extensions of two years at a time may be allowed until you have been in the U.S. for a total of seven years if you are a manager or executive, or for a total of five years if you are a Specialized knowledge employee.
Yes, the USCIS has instituted a program called Premium Processing. If the USCIS is paid an extra $1,000 on a separate check, the USCIS guarantees it will adjudicate the petition in 15 days or notify you if more evidence is needed.
Any person who has worked for a corporation or company for at least one year as Manager or Executive in the preceding three years may qualify as L-1 Executive.