Saving word docx to laptop and opening it in pages

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Pages is not a Word clone and does not open Word documents in their native document mode as would MS Word. Instead, Pages will attempt to open and translate the Word document into Pages internal (.pages) document format, leaving the original Word document unchanged. There is a second translation event when you export that Pages content back to MS Word .docx format. There are features in either application that do not survive the translation process and Apple does not guarantee that accuracy or even a successful translation. Yes, Word documents exported from Pages content may not appear the same when reopened in MS Word.

It sounds to me as you have discovered the catch in using Pages to share documents with faculty that use MS Word, likely due to the institution standardizing on Microsoft Office — much like many corporations. In that case, you don't want Pages — you should be using the same tools as the faculty and that may have been spelled out clearly in course curriculum too.