Not too many mistakes.. good job, Jun! I'm just going to mention that "to improve" can be used transitively and intransitively, so "both speaking and listening are improving" would sound quite natural. As far as gerund (focusing) versus infinitive (to focus), we generally use the gerund before the verb -- as you did here -- nice job! We use the infinitive after the verb as a predicate nominative, eg: "I believe it is also beneficial to conversational skills to focus on vocabulary."

Btw, I don't really think there's a strong relation between vocabulary and conversational skills, except to the extent that you learn the specific vocabulary used to discuss subjects of interest to you, as well as phrases used to guide conversation ("spoken discourse connectors" and such).

As far as dictionaries, I believe your English is good enough that you would benefit from using an "English-only" dictionary, at least, most of the time. There are many good ones on line -- the McMillan gives very good info about how frequent a word is (learning the most common words first is amazingly beneficial to gaining fluency as fast as possible.

Anyhow, I hope this helps, and I wish you luck and continued success!

My next aim for studying English

My stay here in the U.S. is going to be 3 months. I can feel my English conversation skills both speaking and listening have considerably improved. To improve my English, I’ve been spending my time to listen and speak English sentences in CDs. As a next step, I am thinking to focus on studying vocabulary which includes words and idioms.
I consider better vocabulary also improves the conversation skill. So I am using textbooks for that when I have time. To remember English words and idioms which I don't know, translation from them to Japanese, my mother language would be the best way. On the other hand, remembering them only in English, looking up those meanings only in English dictionaries, would also be one of the methods. In this case also, thinking of corresponding Japanese meanings would help understanding.

I’d be glad if anyone corrects my sentences.
Thank you.

My next aim for studying English

I will be staying here in the U.S. for 3 months. I can feel that my English conversation skills (including both speaking and listening) are being improved. To improve my English, I’ve been spending my time listening to and speaking English sentences in CDs. As for my next goal, I am thinking of focusing on studying vocabulary, which includes words and idioms.
I am considering the idea of focusing on vocabulary, which also improves the conversation skill. So I use textbooks for that when I have time. To remember English words and idioms that I don't know, translating them to Japanese, my mother language would be the best way. On the other hand, remembering only in English and looking up those meanings in English dictionaries would also be one of the methods. And in this case, thinking of corresponding Japanese meanings would help understanding.

I’d be glad if anyone corrects my sentences.
Thank you.