I would like you, Writeacher, to check my letter since you know everything about the project and can help me with the word choice. I noticed I wrote two unfinished sentences in the first part of the letter. I'm posting them to you again.
1) I'm terribly sorry I didn't manage to write to you before but I've been very busy both at school and at home.
2) Actually, I'm going through a bad time (or not a very good time?) since my child has just recovered from a bad flu and my mum has nearly lost her voice and her vocal cords are going to be operated on next week.
3) By the way, our science teachers have decided to meet tomorrow to better define the theme and objectives of the project and would like to know a few more things before our preliminary meeting.
4) First, do you still think the project should concern mainly biodiversity in water and other waterways? Do you believe our physics teachers should be involved in the project as well?
5) Some of our science teachers would like to involve a whole second class of students instead of single students selected from different second classes.
See below.
1) To improve the flow and completeness of the first sentence, you could rewrite it as follows: "I apologize for not writing to you earlier, as I have been very busy with school and home responsibilities."
2) To make the sentence more clear and concise, you could rephrase it like this: "Currently, I'm facing some challenging circumstances, as my child just recovered from a severe flu and my mother is scheduled for vocal cord surgery next week."
3) The sentence you provided seems well-constructed, but if you would like a suggestion for rephrasing, here it is: "By the way, our science teachers are planning to meet tomorrow with the aim of further defining the project's theme and objectives. They have requested additional information prior to our preliminary meeting."
4) The provided sentence is clear, but you could refine it by making a slight adjustment: "Firstly, I would appreciate your input on whether the project should primarily focus on biodiversity in water and other waterways. Additionally, do you think it would be beneficial for our physics teachers to be involved in the project?"
5) The sentence is grammatically correct, but you could make it clearer by revising it like this: "Some of our science teachers propose involving an entire second class of students rather than selecting individual students from different classes."