1. Q: 季節の中でいつが一番にぎやかですか。 "Which season is the most lively?" Would I use いつ instead of どれ/何? Also why? Also can I use
   にぎやか to describe the season/time of year as being lively?

いつ、どれ, and 何の would all work. can use にぎやか

 A: はるが一番にぎやかだと思います。 "I think spring is the most lively season."

good

2. Q: せかいのまちのなかでどこがいちかんきれいですか。"What is the most beautiful town in the world?" Would どこ here?

どこ is fine here, but you could also use 何のが

　　A. 白川がいちばんきれいです。 "Shirakawa is the most beautiful town in the world."

	good

3. 私のパソコンはあなたのよりおそいです。　vs 私のパソコンのほうがあなたのよりおそいです。
   I'm trying to translate the sentence, "My computer is slower than yours." I wrote the second sentence, but when I look at an answer
   key it uses the first sentence. Was wondering if my answer was wrong, if the first sentence is more natural, etc.; just need an
   explanation for it.

both versions work, but you dont really need both ほうが　and　より together, so the textbook version is just faster/easier


4. この週末なにをしますか。 "What will you do this weekend?"
   家族とメリーランドに行くつもりです。兄とあそこに住んでいますから。 "I plan to go to Maryland with my family. Because, I will be living
   there with my brother."

good

5. 夏休み/冬休みになにをしますか。 "What will you do during summer/winter break?"
   夏休みと冬休みに兄と電気をべんきょうするつもりだ。"I plan to study electricity (electrician, can't think of a better way to say it so
   I used 電気) with my brother over summer and winter break.
   夏休みに毎日三十分はしるつもるだ。 "I intend to run for 30 minutes everyday during summer break."

all good