Cannot update pages!! Please help!

Since your hardware is not excluded as a 2015 model, there may be some newer features in the Pages document sent you that Pages v5.6.n cannot handle. Word document would be a different story as I suggested.

The key to your student status is to not change anything that works now so that your school related deliverables are not disrupted by the unexpected. Wait until the school year is over, then consider an operating system, and Pages upgrade.

Mojave continues to run 32 or 64-bit applications. Catalina only supports 64-bit applications, and 32-bit applications, and 32-bit printer drivers are a bust. You have to do your homework to see if there are 64-bit vendor replacement applications and drivers available when considering Catalina. See if your printer is on Apple's AirPrint list of supported devices which require no vendor printer drivers for wired/wireless printing.

I have been running Mojave on the Early 2014 Air, and on my Late-2013 27in iMac since Mojave was released. No surprises. Just works.

You would need to be running macOS Mojave (10.14.6), or macOS Catalina (10.15.2) before you can download the Mac App Store pages. Pages v5.6 is the oldest version of Pages that can open a newer Pages document, but that goes out the Window, if your MacBook Pro is a MacBookPro3,1 (June 2007) thru MacBookPro8,3 (Late 2011) model. This hardware range is unsupported in the current Pages documents, and would override your having Pages v5.6 or v5.6.2.

From menu : About This Mac, look at the information in the parenthesis describing your Mac model (shown in the red box for the following example):

If your hardware is too old, have the source for the Pages document send it to you as a Word document.

Welcome.