Though my English isn't advanced yet and there are several ways to say them in Japanese, I'd like to write what I would say. (They are not the direct translations.)
"I hope that you can help me improve my Japanese"
--> 私の日本語がもっと上手[じょうず]になるように手をかしてもらえたら/手をかしていただけたらうれしいです。
"My Japanese is bad so I hope that you can help me improve it"
私の日本語はまだあまり上手ではありません。だから(あなたに)教えてもらいたいです/教えていただきたいです。
"I would love to have a language exchange with you"
--> ぜひあなたといっしょに言語を学びたいと思います。(言語を教え合いたいと思います。)
I wrote in the formal way. If you need more explanations or other translations, please let me know. I hope this was helpful.