It is possible to retain form fields inside an embedded PDF for users to fill in. Such PDFs should display without problems using PDF Embedder; however, there will be no way for the user to enter text into the fields and thereby save their responses. The fields will still be intact for the user to fill offline but you would need another method for the user to submit their responses.
PDFs can be produced that are password-protected so need a password in order to be viewed. No version of the plugin supports this. The PDF Embedder Premium Secure version does allow you to embed a (non password protected) PDF in a WordPress page in such a way that it is difficult for the user to obtain the source PDF; it should also be possible to prevent access to that page without being logged in with an appropriate WordPress account, or to password-protect the whole page.
If your fields are not being retained after embedding, it is likely due to how the PDF was initially created.
MS Office software seems to have problems exporting fields correctly in PDFs. If you believe that you have created proper fields in your Word document, but they just don't seem to be appearing in the exported PDF, please try the following workaround. In Word don't accept the default save as 'Word Document (*.docx)' - instead save the file as a 'Word 97-2003 Document (*.doc)' initially, and then select File > Export as PDF (*.pdf)'. This method also works for Excel Spreadsheets.