Schools will want to see all of your year 9, 10, 11, and 12 grades up to the point of when you submit your early app, which is typically Nov. 1 of your application year. Then if you are deferred or accepted in the early round, you will send in your finally grades and scores as soon as they are accessible. Schools understand this process and it doesn’t present any problems to your application. Remember that when US students apply in the early round, they still have 7 more months of school before they graduate, and submit their final grades in June or early July when they become available, so this is standard.
Regarding a Fulbright equivalent - no, we don’t really have anything that is completely on par with that particular organization. However, the Robertson Scholarship is available to students willing to consider Duke University or University of North Carolina at Chapel Hill, which is a little similar - see this link. https://robertsonscholars.org/apply/international/