Student Aid Improvement Act of 2019 This bill revises provisions related to federal financial student aid. Specifically, the bill replaces the expected family contribution metric with a student aid index used to assess a family's financial need and approximate their financial resources to contribute to a student's higher education expenses. The bill also revises the process for filing a Free Application for Federal Student Aid (FAFSA), and it removes certain eligibility requirements related to drug-related offenses and registration with the Selective Service System. The bill reauthorizes the Pell Grant program through FY2021, establishes a new eligibility formula for Pell Grants, and increases the maximum Pell Grant award. The Department of Education (ED) must conduct certain activities to educate students and their families about Pell Grant eligibility at a younger age. In addition, the bill expands Pell Grant eligibility to (1) certain incarcerated individuals; and (2) students enrolled in short-term programs that provide training in high-skill, high-wage, or in-demand industry sectors or occupations. ED must develop a standard terminology and format for financial aid offers, which shall provide certain information such as costs, grant and scholarship aid, annual net price, work-study, loans, and accepting or declining aid. In addition, the bill provides that a borrower on a 10-year standard loan repayment plan shall not be subject to a maximum monthly payment or any other maximum monthly payment. Further, the bill makes funding for historically black colleges and universities and other minority-serving institutions permanent.