As a foreign student you are allowed to have equity in the company as long as you are not employed by that company. You are legally allowed to own a company as a foreigner, just not to work there. So the myth about you not being able to own equity is b/s.
Honestly, just start your startup, go as hard as hell at it, make money, get funded by a renowed VC firm and if they think you are useful, then they will sponsor you as their employee and you will be legally employed in this country.
Another route is to make so much money that you are given a green card. I believe if you generate more than $1 mil. in rev. and employ 12 citizens (any restaurant can do that), then you'll be all set.
You will not break laws regarding employment by monetizing on the app.