I included the sentences I was most doubtful of. I hope you can clear my doubts. Thank you very much in advance.

1) My family and I have been on holiday in Greece. We stayed on a little island... There wasn't any wind. Unfortuanately I spent there only a week.
2) I have just finished my dinner. I finished "having dinner"
3) I and my family (OR My family and I went to Rome last month.
4) On Monday starts the school. I'm sorry we've never been in touch recently.
She is 15 years old just like us.
I was very sad because I still had to do my homework and study.
What was your holiday like? How was your holiday?
5) I hope to receive an answer soon (your prompt reply, a quick reply from you'') Keep me up to date with what happens to you.
6) I still have a lot of things to study because school starts tomorrow.

1) My family and I have been on holiday in Greece. We stayed on a little island called ... There wasn't any wind. Unfortunately, we spent only a week there.

2) I have just finished my dinner. I finished having dinner. <~~Both are OK.

3) My family and I went to Rome last month.

4) School starts on Monday. I'm sorry we haven't been in touch recently.

She is 15 years old, just like us. <~~OK

I was very sad because I still had to do my homework and study. <~~OK

What was your holiday like? How was your holiday? <~~Both OK

5) I hope to receive an answer soon (your prompt reply, a quick reply from you'') Keep me up to date with what happens to you. <~~All are OK.

6) I still have a lot of things to study because school starts tomorrow. <~~OK