(SPOILER)
1. What was the group that Lightning worked for before the fal'Cie accident in her hometown?
The Guardian Corps.

2. What was Hope's hometown?
Palumpolum

3. What catalyst is needed to upgrade the axis blade?
Perovskite

4. Who battles with Hope against Alexander?
Lightning

5. The Fal'Cie Carbuncle is responsible for what kind of production?
Oh god I don't know