It's a special sound, in IPA it's called ɕ and I don't think you have it in English.
Wikipedia page for the sound: http://en.wikipedia.org/wiki/Voiceless_alveolo-palatal_sibilant
Hear a native speaker say the word here: http://sv.forvo.com/search-sv/kyckling/
Neither. It's a vowel sound that English doesn't have: a rounded I-sound. Wikipedia has some useful sound examples of the Swedish vowels: http://en.wikipedia.org/wiki/Swedish_phonology#Vowels
Neither really, the sound is called [ɕ], also see my other comment about it on this page: https://www.duolingo.com/comment/5524686$comment_id=8575308 (answer to TwoWholeWorms)