Google creates in your email folders/labels a special folder with the date and time. The folder name is “Moved.” Don’t worry, the original copy remains in your school inbox. After the content arrives in your inbox, you will see a new folder or label.
You will see a copy of your email in the box. Once you have the emails in your inbox, you can move them to whatever other folder or label you want them to be in (e.g. “School”). Since you can run this process daily, you can clean out your inbox with the same frequency.
For Google Drive, you will see something similar. Depending on the quantity and type of files, the process can take longer.
The old Google Takeout makes it easy to save all your Google content as files you can save on your computer or a USB external flash drive. The main benefit is that it lets you get copies of much more than Drive and Gmail. You can get Google Photos, Google Sites, Blogger posts, etc.
While it works well, you are going to need a program like MS Office 365 to open the files. You may want to rely on a free, open source solution (FOSS) solution like LibreOffice, OpenOffice, or NeoOffice. All of these work on Windows, Mac, or GNU/Linux operating systems, but not Chromebook.