It's answer time! Many thanks to those who have replied.
1. When Japanese-speakers name the four seasons, which season always comes first? Just for practice, write all four in the proper order.
春夏秋冬（しゅんかしゅうとう）。 Note that small kids read this はるなつあきふゆ.
2. In what month does the academic year for schools as well as the fiscal year for most organizations start in Japan?
4月。
3. What is the spring's first strong gust of wind that is said to bring the season called in Japanese?
春一番（はるいちばん）。
4. What is the other meaning of さくら other than the cherry (tree or blossoms)? For that meaning, the word is always written in kana.
露店（ろてん）などで、客の買い気をそそるため、客の ふりをして買い物する仲間。
A decoy, a plant, a shill, a claqueur, etc. Anyone who is hired to pretend to be a customer for the purpose of attracting other customers.
5. What kind of meat is called 桜肉?
馬肉（ばにく）。
6. What is the word for "spring rain" and what's its exceptional reading in kana?
春雨（はるさめ）。
7. What is the other meaning of that word above? (Hint: food)
透明な麺(めん)状の食品
Tranparent noodle often used in salads.
8. 「春が来る」 has two completely different meanings. Its literal meaning is obvious. What is its figurative meaning? If you're willing to, give me an example sentence using the phrase for that meaning.
「人に幸せが訪れる」という意味です。"A happiness (usually a romantic one) comes to someone."
「35年間ボーイフレンドのいなかった花子さんにやっと� ��が来ました。来年結婚する予定です。」
9. Name a few seasonal words for spring that are used in haiku.
春風、春雨、残雪、花見、卒業、進級, etc.
10. Why does the spring break please many Japanese students when it's considerably shorter than the summer break? (This is related to question #2.)
多くの学校では春休みに宿題が出ないからです。
Because most schools don't give homework for the spring break as it falls between two academic years.
Thanks again for your replies. See you in three months in the "Summer" Pop Quiz! これからもがんばって勉強してね～。
