Does it matter that the gate faces the library door or the children's room?

it's best not to, because, according to people's usual attention direction, when a guest enters the door, the first thing he looks at is the direction facing the door. However, it's ok if you don't put anything in the study that is inconvenient for others to see. For children, you still have to take care of them nearby, and they are far away. Suppose there is something uncomfortable, you can find it in time.