Dear Mohammad,
Good day, thanks for querying in this forum. We’re happy to help you.
From your description, it seems that you want to use your school account to install free Office applications in Windows 7.
If my understanding is right, for your first question, currently, we’re afraid that there is no such free Office applications for students. Generally, after registering as Education account, you need to contact your Office 365 administrator to assign “The latest version of Desktop App” license to you, then you can install Office 365 office applications. Otherwise, you cannot install or activate office applications. You can choose to use Office for web, and it is free for all Microsoft office users. Free Microsoft 365 Online | Word, Excel, PowerPoint
At the same time, if you have license “The latest version of Desktop App” to install office, according to official article: Windows 7 end of support and Microsoft 365 Apps - Deploy Office | Microsoft Learn Microsoft 365 Apps is no longer supported on Windows 7. Version 2002 is the last version of Microsoft 365 Apps that's available for devices running Windows 7. This means that if you want to use Microsoft 365 Apps on devices that are running Windows 7, you need to use Version 2002. If you try to install a newer version of Microsoft 365 Apps, such as Version 2201, on a device running Windows 7, you'll receive an error message. For more details, you can refer to this thread: Office 356 won't install - Microsoft Community
For your second question about “sign up at office 365 education”, does it mean that you have been required for verification code from your school account? If so, you can go to your email with your school account to get your verification code instead of contacting your school.
If the scenario above is not consistent with yours, you can also post back and provide the screenshot of “its asking for the verification code send to my school's email adress”?
Your understanding and patience will be highly appreciated. I hope that you are keeping safe and well!
Sincerely,
Sukie | Microsoft Community Moderator