Others PG Courses at Stanford University

Yes portfolio is important requirement that you must provide Stanford University if you need admission in Design course. You should have already mastered some basic skills that you can bring for the program such as quick idea sketching, product rendering, prototype building, etc. 

GMAT scores are one of the crucial criteria during admission and are submitted by students to improve their profiles. 58% class submitted GMAT scores, and 42% submitted GRE scores. There is no ideal score provided by students to get into the Stanford MA. According to the university student profile 2

As per a ranking body, Stanford is popular for many programs like International Education, Art History, Asian Studies, German Studies, History, and more. Students can check some popular MA programs at Stanford along with the tuition fees:

No Stanford Design programs are not yet offered at PhD level. The highest level in which Design courses are available is Master level. But the curriculum of MS Design program is such that you can smoothly shift to another Ph.D. programme in Science or Engineering field. 

Stanford University does not mention it anywhere that students must have prior experience or employment in Design to get into Design program. But university expect or want students to try to make impact the world through design and design thinking.