1. You may remain in the United States with a pending Form I-485. While you will not hold an immigration status, you are allowed to remain in the country until your application for adjustment of status and will not accrue unlawful presence.
2. EAD approval does not provide a basis to remain in the country. You are simply authorized to work for a certain period of time. In your case, you would be authorized to work while your green card application was pending. In addition, an approved EB-1 petition conveys no right to stay in the country.
3. You are not required to hold a job at all during the green card process.
Keep in mind that you may linger be able to adjust status if your employment is terminated. You should consult an attorney as soon as possible to plan what to do if your employment is terminated. You can read more about adjustment of status at http://myattorneyusa.com/adjustment-of-immigration-status.
Answered on Jun 27th, 2016 at 2:11 PM