Yes, it's correct. Thank you very much.

I urgently need you to check this paragraph.

1) Here below you can find the list of the students you sent me. I pair each of your students with an Italian partner for the email partnership.
2) You should send me as soon as possible the email addresses of the students typed in bold (7 in all), so that my students can start sending email to them, too.
3) I really hope you can help us carry out (fulfil) this project (???). I’m sure this initial partnership will lead to further projects to be carried out in the next years.
4) Looking forward to receiving your next email, I hope you had a nice Easter among your friends and family.

1) Here below you can find the list of the students you sent me. I have paired each of your students with an Italian partner for the email partnership.

2) As soon as possible, you should send me the email addresses of the students typed in bold (7 in all), so that my students can start sending email to them, too.

3) I really hope you can help us carry out this project. I’m sure this initial partnership will lead to further projects to be carried out in the next years.

4) I hope you had a nice Easter with your friends and family, and I'm looking forward to receiving your next email.

Here's the corrected paragraph:

1) Below, you will find the list of students you sent to me. I have matched each of your students with an Italian partner for the email partnership.
2) Please send me the email addresses of the students typed in bold (a total of 7) as soon as possible, so that my students can start sending emails to them as well.
3) I sincerely hope that you can help us carry out this project. I am confident that this initial partnership will lead to future projects in the coming years.
4) I look forward to receiving your next email. I also hope you had a wonderful Easter with your friends and family.