In a Two-Headed Giant game, Ghirapur Orrery's second ability triggers for each player on a team separately. If one player has cards in hand, it can still trigger for the other player.

The draw step is after the upkeep step, so drawing a card as a turn-based action won't affect whether Ghirapur Orrery's second ability triggers.

Ghirapur Orrery's first ability allows a player to play an additional land during their main phase. Doing so follows the normal timing rules for playing lands.

If the player has any cards in hand as Ghirapur Orrery's second ability resolves, the ability does nothing. Notably, a second Ghirapur Orrery won't have a player draw another three cards unless the player empties their hand after resolving the first one's trigger.

No player may take actions in a turn before Ghirapur Orrery's second ability checks to see if it should trigger. If the player whose turn it is has any cards in hand, it won't trigger.

Ghirapur Orrery's first ability is cumulative if more than one is on the battlefield.