Please could you check the accuracy of my Japanese?
Does this sound ok?
この2ヶ月、私は試験で忙しかったので、みうさんとあまり知り合わなくてしまった、すみません。一人でロンドンへ引っ越しして、ロンドンの生活になれて、日本の文化と違って、少し大変かもしれないね。これから私はひまだから、いっしょに何かしない? ロンドンを案内して、いろいろなおもしろい場所を紹介することができるよ。そして、英語の練習ができる。
ところで、みうさんの名前の漢字は何?
I want to say something like: "These past two months, I was busy with exams so unfortunately I haven't really gotten to know you Miu, I'm sorry. You moved to London alone, adjusted to London lifestyle, and the culture is different to Japan, so it may have been difficult, right? From now on, I am free, so shall we do something together? I can show you around London and introduce you to various interesting places. Also, we can practice English.
By the way, what are the kanji in your name, Miu?"
Please let me know where I have made mistakes, and how I can amend them. I'm still at a basic level of Japanese, so I'm trying to use quite simple grammar.
Thanks!