No, you can’t. Since you are not authorized to generate any kind of income, you cannot run a business from your office or home. However, according to the new regulatory changes, effective May 26, 2015, eligible H4 candidates can file the form I-765 to receive an authorization to work and receive a salary in the United States. However, whether you receive the EAD or not, you are able to study in the US in any field. If you need further information on this, schedule a consultation with a reliable immigration lawyer at (718) 924-2896.