At the start of the sub-game both players draw their initial hand (usually 7 cards). If one player has fewer cards than required, that player loses. If both have fewer than required, both players lose.
Events in a Shahrazad sub-game do not normally trigger abilities in the main game. And continuous effects in the main game do not carry over into the sub-game.
You randomly chose which player chooses to go first or draw first.
At the end of a subgame, each player puts all cards he or she owns that are in the subgame into his or her library in the main game, then shuffles them. This includes cards in the subgame's Exile zone.