Yes Microsoft Word can open LibreOffice Writer documents in the odt format, unless it's a very old version your school has. You can also open Microsoft Word (doc, docx) files in LibreOffice Writer.
You can choose whether you save the files you create in LibreOffice Writer, as Microsoft Word files, doc or docx, or save them in the native odt format of LibreOffice. Beware though, that some of the formatting may not be preserved, when saving LibreOffice Writer files as Microsoft Word files, and vice versa.
I have often worked with the same documents in both Microsoft Word and LibreOffice LibreOffice, and don't recall running into any problems, moving between the applications.
What I have said also applies to spreadsheet documents, in Excel and Calc, as far as I can remember.