Twenty Minutes at the Minami Library

She can return the two books at the counter, since the return box is prohibited (入れないでください). She should then make a card at reception, because borrowing requires one. Next she can copy two pages at the counter for 20 yen, and finally borrow up to three books for two weeks. She cannot drink the tea inside (飲んではいけません), so she must drink it outside. Order matters: borrowing is only possible after the card exists, and the 7:00 closing leaves no room to waste.

なくてもいい removes only one specific obligation: showing the card when returning. The notice separately says 借りるとき、カードが要ります, so a card is required to borrow, and it is made at reception. The two sentences cover different actions, and reading them as one causes the error. She still needs a card for the three books; she simply does not have to present it at the return step.

Two pages at 10 yen each is 20 yen, paid and requested at the counter (カウンターでお願いします). The return box is closed to her because the notice says 入れないでください, a prohibition, not a preference. That matters practically: counter returns take time from her twenty minutes, and the counter is also where the card and copies are handled, so she should combine all counter tasks in one visit rather than queue twice.