Can an individual submit an application if he/she has applied for permanent residence but has not yet received approval as a permanent resident of the U.S.?
In general, when U.S. citizenship or permanent residency is required, the requirement must be satisfied at the time of award, not application submission. Each funding opportunity announcement (FOA) addresses this in Section III. For a list of current NRSA fellowship FOAs, see the F-Kiosk: http://grants1.nih.gov/training/F_files_nrsa.htm.