If you open a document on Google Drive, then it remains on Google Drive. Whoever created it can certainly edit or view it, and they can also allow other people to edit or view it. They presumably gave you permission to view it, or there wouldn’t be any point sending you the link, and they may or may not have also given you permission to edit it. They could also have given these permissions to any number of other people.
Given any Google document that you can view, you can also download a copy of it, in a variety of formats. For a word processor document, you can choose to download it in Microsoft Word format, or PDF, or a few others. For other sorts of documents, precisely which formats you can download it as will vary, but there will always be that option. Once you download it, the copy that you have on your machine is yours, and you can do whatever you want with it. Nothing you do to your copy will affect the copy on Google, and nothing anyone does to the copy on Google will affect your already-downloaded copy.