Yesthe Boren (usually sophomores) and Truman (juniors) are for non-senior applicants.
Each of the scholarships will list a GPA minimum, so consult the relevant websites. As a general rule of thumb, though, Messiah students should have a GPA of 3.90 or close before considering applying.
They are extremely important. There are many very bright students in the world; what will distinguish your application is evidence of your initiative outside of the classroom. In particular, most scholarship committees look for evidence of leadership they want to know whether you have identified a compelling problem/issue and how you have mobilized resources to address it.
No, not while you are an undergraduate. All the listed scholarships require an institutional endorsement of your application.
Yes. Many of the listed fellowships permit recent graduates to apply. Typically the only restriction is an upper age limit. Messiah's scholarship advisor is more than willing to help students with their applications even if they have graduated.
Yes, in certain cases. For instance, the Gates Scholarship at Cambridge University has no citizenship restrictions. With respect to the Rhodes Scholarship at Oxford University, several countries offer the award, not only the US; you might be able to apply from one of them if it is your country of nationality.
Scan the relevant websites listed on Messiah's fellowship page and determine the places and programs of study that are most appealing. Then schedule an appointment with Messiah's fellowship adviser, Dr. John Harles, to consider which fellowship best meets your interests and abilities.