I suspect Times New Roman font is the default font-family for the document used. When content from MS Word is being pasted, the transferred data has no information about the default font-family that is used in MS Word. Therefore, it does not apply one in the pasted HTML content.
The applied font in such case is the default for the browser or, the page's default font size. The demo page have Segoe UI font as default and this is the default font-family that is applied and shown in RadEditor.
As for attaching an MS Word file, you can just add it to a zip archive and attach the zip file to your message.
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