Trouble with the usage of ずつ translating my own sentences

Question

I am trying to write the following sentences in Japanese:

Everyday I try to have 3 non-consecutive study sessions, each taking 3 hours.
Moreover, I'm trying to make sure that I learn at least 20 unknown words in each of those 3 hours.

Honestly, I fear that even the English ones above may have errors and/or sound unnatural. In any case, below is my attempt at expressing them in Japanese:

僕は毎日非連続的な勉強時間を三回三時間ずつしようとしています。
さらに、その三時間ずつにまだ知らない単語を少なくとも二十個覚えるとしています。

*I know they must be horrendously unnatural, and full of erroneous grammar. I am at a stage where I can somewhat read simple articles in Japanese with a dictionary handy, but can hardly even make a proper, simple sentence myself without dying a little inside.

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My biggest problem here is where to place ずつ exactly. Moreover, I am aware that sometimes it can be omitted, thus making it even harder to use.

In English, if I were to say "I study for three hours each day," each modifies day instead of hours. However, in Japanese, it'd be something like:

一日に三時間（ずつ）勉強する。

*Hopefully, this one is error-free.

Here ずつ modifies 時間 instead. I would've put ずつ after 一日 if I hadn't seen this sentence.

On the other hand, I have little problem using ずつ in this situation:

一人ケーキ一個（ずつ）取って下さい。

Again, here I believe ずつ is optional. In this case, ずつ follows 一個, and I think the English equivalent can be either "everyone take one cake each," or "each one take one cake."

Please help me correct my sentences. 教えていただきたいからです、お願いいたします！

*I'm not sure if this counts as a translation request, but if folks here think it does, I apologize beforehand. I'll remove it myself then.

Answer 1

You rendered "Everyday I try to have 3 non-consecutive study sessions, each taking 3 hours" to 僕は毎日非連続的な勉強時間を三回三時間ずつしようとしています, which has 2 major problems.

First, 勉強時間を…する doesn't really make sense. It should be 勉強時間を…持つ or 勉強を…する. Second, you should use しようと思う rather than しようとする (unless this is an excuse or something, which objectively explains your situation) because you are exactly the one who has the intention. You should express it subjectively. (This has something to do with problems of perspective and position like restriction for other person's emotion in indicative mood or usage of やる or くれる.) e.g 私は勉強時間を非連続的に毎日三回（それぞれ）三時間ずつ持とうと思っている

As for the second sentence: "Moreover, I'm trying to make sure that I learn at least 20 unknown words in each of those 3 hours", you should use ずつ in this way: その３時間ごとに…単語を２０(ずつ)覚える. (Counter for 単語 or 言葉 can be either 個 or the generic counter, and ずつ here is optional.)

You can express "to make sure that" as …ようにする, so, all in all, it's 「さらに、その３時間ごとに、まだ知らない単語を２０個ずつ覚えるようにしようと思っている」.