They are both national libraries and have been around for a long time.
Answer:
"La comida" is the best response
¿Puedo ir a estudiar a la biblioteca? When there are two verbs in succession, only the first should be conjugated. Puedo is first person singular present, so that is the correct answer.
The correct answer would be
2. Nos
3. Me
4. Os
5. Te
6. Se