If you have an EB-1A-based EAD and a pending I-485, starting an unrelated business (such as teaching) is risky. Your EB-1A petition asserts that you intend to work in your field of extraordinary ability. Shifting to an unrelated field could raise questions about your original intent and impact your green card application.
Additionally, traveling on Advance Parole in this situation may pose some risks. It’s advisable to either have a job offer or a clear plan to work in your field (such as consulting with clients) before traveling. Proceed with caution.