I am an H-1B holder who has filed an I-485. What is my status if I travel abroad and use my Advance Parole to reenter the United States? Should I use the EAD to work for my H-1B employer?

You can work for your current H-1B employer without using your EAD to preserve your H-1B status. If necessary, your current employer can apply for an extension of your H-1B status. If you will use your EAD to work for your sponsoring or any other employer, you will lose H-1B status and you will be in pending I-485 status.