A: No, absolutely not. But, you probably ought to have it, anyway.
Need is a strong word, and there are plenty of viable alternatives to Microsoft Office. LibreOffice, the free and open-source office suite, is well-suited to legal work (indeed, I used its predecessor, OpenOffice.org, in my litigation practice for years). So is Apple’s iWork suite. Google Docs has come a long way, and while I would still like to see some improvements, most lawyers will be able to get their work done in Google Docs quite happily.
Still, you should probably have a copy of Microsoft Office if you are going to share documents with people who use it. LibreOffice does an excellent job editing documents created in LibreOffice. The same is true for iWork and Google Docs. What they do not always do excellently is edit documents created in Microsoft Office. This is especially true for legal documents, which often contain a lot of ad-hoc formatting (using spaces for indentation or tabs for alignment, for example). Even simple things like signature blocks rarely come through as intended.
When you receive a document created with Microsoft Word, you should be prepared to open it in Microsoft Word, so you can see it as intended. Likewise, if you are going to share an editable document with someone, you should share it in a format they will be able to use. With my clients, I often use Google Docs, since all of them have Google accounts. But with other lawyers, I always default to Word.
So the answer is no, you do not need Microsoft Office. But you should have it, anyway.