Noob questions

[Enkidoh]

Yeah, the quest information for the Lightning events are not really that helpful sadly, but what you have to do is participate in one of two particular FATEs that spawn in those locations - one against a group of giant crabs in Three Malm Bend in Middle La Noscea, and the other against a giant dodo NM called 'Gluttonous Gertrude' in Quarterstone in Western La Noscea (this is what the quest info means about 'monster culling operations').

During one of those FATE battles, there is a chance that Lightning may appear in the battle, which you can tell by the FATE battle music suddenly stopping and changing to FFXIII's battle theme 'Blinded by Light', and dialogue from Lightning occurs during the battle. Ensure you can get enough hits in on the enemy and you should get a gold medal at the end, plus two special items called 'Otherworldy Parcels'. The Journal entry for the quest should also update with confirmation that you've completed that step.

Then simply trade one of the parcels to the reporter NPC who gave you the quest and he'll give you Lightning's gloves in return. To get the weapons, you need to keep doing those FATEs above (Lightning will still randomly appear in them even if you've completed that quest and will still reward you with the parcel items), and then just trade the parcels to the 'herald supplier' NPC next to the npc you got the quest from, each FFXIII weapon requires one parcel, so you really only need to do the FATEs again another four or five times to get all of them.

Hopefully this has helped.