Are you applying for admission as a graduate student, or as an undergraduate? If you are a grad school applicant, you need to check Stanford’s policies about funding international grad students. They may be significantly different from the policies about funding undergraduates.
In either case, in order to get your student visa you will need to present evidence that you can cover all of the costs of your education and living expenses for at least the first year. For your partner to be able to accompany you with an F2 visa, you will need to be legally married, and you will need to present evidence that you and your partner together have resources enough to cover your partner’s full costs as well.