Short answers, pulled from the story.
Writer Gen Urobuchi created Kyubey for the 2011 anime series Puella Magi Madoka Magica. Producer Atsuhiro Iwakami stated that the mash-up of cuteness and darkness is the central theme to the show.
The Incubators use converted emotional energy to counter entropy and prevent the impending heat death of the universe. Their true goal in creating magical girls and witches is to stave off the heat death of the universe.
Kyubey won the 1st Newtype Anime Awards for Best Mascot Character in 2011. They took third place and fifth place in the following two years during 2013 and 2014.
Pubescent and prepubescent girls produce the most energy which reaches its zenith when a magical girl's soul gem turns into a grief seed. The Incubators developed technology to convert emotions into energy for their survival.
A large amount of merchandise based on Kyubey has been created by various manufacturers including nendoroid figures produced by the Good Smile Company. This commercial success established him as an iconic mascot within the anime industry.