In your situation, when filing the I-130/I-485 package for his green card, you should use form I-864 or I-864EZ, as appropriate, not form I-134, which is only for nonimmigrant visas.
You can apply for an EAD extension at any time within 4 months of the current EAD's expiration. Departure while the I-765 is pending does not constitute abandonment of the application.
On May 17, 2007, the Department of Labor published a final rule (Labor Certification for the Permanent Employment of Aliens in the United States; Reducing the Incentives and Opportunities for Fraud and Abuse and Enhancing Program Integrity) in the Federal Register which took effect on July 16, 2007. Among the new rule’s changes is a provision which prohibits the sponsored employee to pay for any fees associated with the filing of his/her application for permanent labor certification, including...