The question you have posed is more a matter of technical definition and protocol that is defined according to the guidelines of each school or scholarship program.
Each foundation or program gives more specific details and definitions for their purposes, which can be dealt with at the time you apply as you indicate. In general, his designation is a general categorization that might be helpful in finding designated programs for persons of "Hispanic" identity.
I was not familiar with the US government definitions, so I did some checking on the census web site.
I suspected, and found it confirmed, that the census guidelines do not give instructions on percentages or other objective criteria. The deciding factor seems to be the individual's sense of self-identity.
The wording in the census guidelines are "those who classify themselves" as in the "Hispanic or Latino" category. I have included below some sections defining the categories and terms below. Note that the census says a person can choose more than one race on the census form.
It seems if you feel mostly identified with his Hispanic background, that would be an appropriate choice. Culture and language should be considered. Do you speak Spanish? Do you speak Spanish at home? Perhaps bilingual? What language do you speak with your grandfather, for example?
On the other hand I know many Hispanic-surnamed people who no longer speak Spanish, but do relate at a broader level to Hispanic history and culture. Perhaps they are Hispanic still.
The second question is trickier. It would be hard to argue that you suddenly became hispanic in your identity, and would smack of positioning or pandering for the purpose of gaining some kind of ethnic advantage by being in an under-represented class. If the question is with which ethnic group you identify, then it sounds like you have already answered your question in prior applications as caucasian. Identifying with an ethnic group from your family heritage and culture is not an exact science, but you may be challenged in trying to justify changing your status with the same school. For new applications, you could give it a try, but only if you can represent the culture and truly bring something to the table of value therefrom.