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 they own that are in the subgame into their library in the main game, then shuffles them. This includes cards in the subgame's Exile zone.