1) Is there a difference between a play, game, and sports?
In psychology and ethology, play is a range of voluntary, intrinsically motivated activities normally associated with recreational pleasure and enjoyment. Play is commonly associated with children and juvenile-level activities, but play occurs at any life stage, and among other higher-functioning animals as well, most notably mammals.
A game is a structured form of play, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more often an expression of aesthetic or ideological elements.
Sport (British English) or sports (American English) includes all forms of competitive physical activity or games which, through casual or organised participation, aim to use, maintain or improve physical ability and skills while providing enjoyment to participants, and in some cases, entertainment for spectators.