Solutions

Question 1: 1975

Question 2: Osamu Dezaki (Who is not Osamu Tezuka, the father of Astro)

Question 3: Osaka (as we can see the Tsutenkaku Tower in the numerous shots of the city)

Question 4: Arikura (Orihara is Kaoru's family name, and there's no Harada in Oniisama E)

Question 5: Porno writer

Question 6: Verlaine

Question 7: The nailpolish on her indexes

Question 8: Sébastien

Question 9: Basketball

Question 10: Kaoru tells her (right after after she reveals her disease)

Question 11: Halloween

Question 12: Home-made cookies

Question 13: Medusa

Question 14: Little glass objects

Question 15: Motomashi Station (if you look carefully when they go to take the train in some episodes, you can see the board with the name)

Question 16: Koneko-Chan (meaning "kitten")

Question 17: The flower arranging club (though she first said she would join the cooking club with Tomoko)

Question 18: Shall I compare thee to a summer's day?

Question 19: Orange

Question 20: Darjeeling tea