The university at which a student is placed will only know of a student's scholarship award if they are informed somehow; typically this is done by the individual NROTC units, but there's definitely nothing wrong with a student contacting admissions or their individual counselor to alert them to the scholarship. However, the Navy does not officially notify schools of scholarship placements during the selection process, meaning options #2-#5 will defintely not find out unless you let them know.
As far as a scholarship's ability to have an impact on the admissions decision, it defintely varies from school to school. It often has a larger impact at expensive, private schools, as they are looking at the 100% tuition piece and the merit/need-based aid money they can now save on that student. However, a student still needs to be within the realm of academically qualified for the particular university.