Hi angad27 -
1. The GMAT costs $250. You may register through mba.com. Your scores will be sent to your 5 schools that you select on test day, and will be valid for 5 years.
2. Our expertise is centered on the GMAT, but I can address your question about extracurriculars in broad strokes... Demonstrating some achievement outside of the classroom is generally an important part of your application. Given the competitiveness of the HBS 2+2 program and the fact that candidates apply while in undergrad studies, I expect that this would also be true for this program. In other words, to gain acceptance to HBS, your application will need to include more than a great GMAT score and your coursework.
3. There are folks in the admissions consulting forums who could give much better feedback than I could on specifics such as this. I'll defer to the gmatclub experts there.
Thank you,
Chris