The phrase "that hasn't been chosen this turn" refers only to that specific Galadriel, Light of Valinor. If Galadriel leaves the battlefield and then returns to the battlefield later in the turn, it will be a new object with no memory of the modes chosen when it was previously on the battlefield.

If all three modes have been chosen this turn, Galadriel, Light of Valinor's triggered ability is removed from the stack with no effect.

It doesn't matter who has chosen any particular mode. For example, say you control Galadriel, Light of Valinor and have chosen the first two modes this turn. If an opponent gains control of Galadriel, that player can choose only the third mode this turn.

If multiple creatures enter the battlefield simultaneously, you must still choose different modes for each instance of the triggered ability that's put onto the stack. If more than three creatures enter the battlefield simultaneously, that choice is made only for the first three.