It works in all maps that drop affection items, from wednesday dailys to challenge quests to event maps.
The effect does not stack with multiple Cuteries.

Affection items are Bouquets, Crystals, Rubies and Diamonds. There are other units that increase drop rates of other items, like Monica increases Demon crystal drop rate, theres a bandit that increases fairy drop rate and Betty (once awakened) who increases gold.

Lastly the 2% increase is a good one, as if the item has a low drop rate, it can increase the chance of you getting it from 4% to 6% with Cuterie in your party.
While this doesn't affect you it makes fairy normal have a better drop rate of rainbow fairys than hard does when you have the bandit that increases drop rate.