How can I work under an E-2 visa while I-485 is pending?

USCIS seems to recognize a limited dual intent for E-2, but the consulate does not. So a visa renewal may be tough but continuing your status could be OK.

Yes, that should not be a problem. I would not travel internationally though until your travel permit comes as the E-2 is not a dual intent status.

You should file an extension of status to keep your E-2 going. Otherwise, you will have to stop working until you receive your EAD.

If you have a valid E-2, you can continue to work for the E-2 employer while your adjustment is pending.

Yes, you can continue to work under your E-2.

If your E-2 is expired, and you have no EAD then no, you are not authorized to work based on the E-2 visa.

In order to remain in valid E-2 status, your I-94 must be valid. The validity of your E-2 visa is irrelevant for the issue of status maintenance. Based on the info you presented, you will not be eligible to work once the I94 expires. You did not indicate having applied for an EAD but that is what you need to apply for in order to become eligible for work while I-485 is pending. E-2 extension does not seem an option here.