How can I start studying on a pending EAD and pending I-485 for EB-5?

Yes, you can study in the U.S. based on a pending AOS (I-485). I always recommend trying to maintain the underlying status (H-1B) as long as possible in case the I-485 is denied for whatever reason.

You may study with a pending I-485 since you will be in a period of stay authorized by the attorney general, assuming I-485 is timely and properly filed. Conservative approach would be to continue to maintain an underlying nonimmigrant H-1B status until you get an approval of your I-485. In case something goes wrong with I-485 and it is not approved, you will fall on your underlying H-1B status. Otherwise you will fall out of status.

Yes, once you have the receipt for the I-485, most schools will accept you to study. However, confirm with your school what documents they will accept since many schools have different views.

A properly filed I-485 provides a period of authorized stay; not any specific status but a period of authorized stay during which unlawful presence does not accrue. Your school of choice may or may not accept you in such status.