When you leave a school, your Google Account will sooner or later be deleted. All of those assignments and communications will be deleted as well, unless you "liberate" your data.
The easiest way to download your files is export them. Select the files you want, click Download... on the right hand side, choose a format for each file type, and then click the Download button. Your browser will then download a zip file containing those documents.
If you want to keep your email, you'll need to need to set up a program (or another online email account) to download your messages via POP. If you want to save copies of your contacts and filters, there are also tools for that on the related Data Liberation page.
Again, dataliberation.org has a tool for "Escaping from Google Sites".
The best way to save your blog posts is to invite yourself as a collaborator, using a regular Gmail account (that you can create for free if you don't already have one). From the basic settings page of your blogger.com blog, click Add authors and type your gmail.com address (or the address of whichever Google account you will be able to use after you leave the school).
You can also follow the steps here to export your blog content.