It depends! Generally, there are two ways to get work authorization in the United States, either through filing an I-765 application for employment authorization (which is usually tied to certain nonimmigrant or immigrant statuses) or through a nonimmigrant visa. You will want to explore your specific eligibility and determine whether your circumstances are better suited for an EAD (I-765) or a nonimmigrant visa (NIV). I would speak with an immigration attorney to figure out what specific visas/EAD classifications you are eligible for.

Why not? If you meet eligibility criteria through a visa, asylum, or another approved status, of course you can.