Can the first player choose where to put cards down?
They are placed left-to-right.
Although you are correct that the rulebook is not completely explicit on this point, the example given on page 8 provides the answer.

In a 4-player game, draw 4 Lesson cards and place them on the first row of the board as follows: the first and second cards face-up, the third card face-down, and the last card face-up.

The key is that the third card is the one that is placed face-down, as shown in the third space on the play mat. If you could choose the order, it wouldn’t always be the third card that went face-down.