several questions about writing an apology letter

I lost a book borrowed from my friend. When I write an apology letter, I feel confused in the ways:
1. In an apology letter, which is more common begin with, a statement of regret, a statement of appreciation or a question? For example, I lost a book borrowed from my friend. If I wrote:
1) I’m sorry I lost your book borrowed two months ago.
2) Do you remember the book I borrowed from you two months ago. I’m sorry to tell you that I lost it.
3) Thank you for lending me your book. But unfortunately, I lost it.
Of these three beginnings, which is more common in your opinion? Thank you.
To be concise, I think “to tell you” is a little wordy because I’m writing to “you” , I’m talking with you, so there is no need to write “to tell you”. What is your opinion?

2. In the middle of the letter, I think the sentence "I know you understand me" is a little direct. Will it better if I change it to "I hope you will understand me".

3. Maybe there are problems in the terms of grammar, but when I read it, it sounds unnatural. Could you help me check in terms of language style? Thank you.

I’m really sorry for losing your book which you lent to me 2 months ago. I have ready to return it to you tomorrow. Unluckily, I realized that I lost it by mistake during my moving to this new apartment a week ago. I know this book means a lot for you. Please give me a chance to make up to you. How about buy a new one for you ? I just have been told that there is a special bookshop which I can find this book. I promise to get the book and give it back to you as soon as possible. I hope this won’t upset you that much. I hope you’re not too mad at me.