The Disney Springs (shopping mall) shuttles only go to Disney resorts. Each resort has transport to a park. Not sure if they validate your stay to ride them. Too slow anyhow. Better to drive and pay the parking fee or use taxi/Uber.
No they don't but do partner with third party. They no longer offer shuttles to the parks from Disney Springs
It depends on where you are, but if you are in Disney Springs then you have shuttle to the various animal kingdoms
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