Generally speaking, when you copy from a web page, Firefox puts the literal HTML on the clipboard. If the page author created a global style rule to apply Times New Roman to the text, but this isn't embedded in the selection, then Firefox doesn't put it on the clipboard.

When pasting, if the HTML on the clipboard doesn't specify a font, Outlook and Word normally use whatever their default font for pasted text is. You can change the default font in Outlook and Word from Calibri to Times New Roman. (Not that I remember where to do that...)

Depending on how often the font is specified in Outlook and Word, I've specified Times New Roman in several places as "suggested" by Microsoft and others.

I'm open to other suggestions.