You've asked a number of related questions. I will address them one by one.

Here are some links that may help:

	Sections / Headers and Footers in Microsoft Word (Ribbon Versions)
	FileName and Path Add-In
	FileName in Footer Template
	Supplemental Header/Footer Building Blocks

 

1. What's the fastest way to add the file name and path to documents?

There is no single fastest way. There are a number of ways. In the menu versions of Word (97-2003) there is an AutoText Entry for this.

You can create your own AutoText entry with the field if you want. You can find an example in the downloads page. That includes a footer building block with FileName and Path field.

You can use a macro with a keyboard shortcut to insert this. An example is available in the Filename and Path Keyboard Shortcut Add-In.

2. Is it possible to set a style in the footer - say 'calibiri 10'?

Yes, there is already a style in the footer called the footer style. You can modify that to your font if you wish. Or you can create a new style. Understanding Styles in Microsoft Word

3. Is it possible to set up a draft doc so that every time I open a new doc it automatically puts a footer in?

Yes, this is called a "template." Templates in Microsoft Word
Look in my Add-Ins folder for the FileName and Path in the Footer Template.

(or is there another way to automatically put footers with the file name and path in every document?)
Yes, but this is harder.
Download Easy New Document Add-In for an example of how to do this.

4. I'm sure I recall in older versions of Word that the filename and path would change on the footer if you moved the document to a different folder. Is that still possible? I can't find a way.

Yes and no. Again, this is the Filename field in the footer. It does not update when you save the document in a different place, it will normally update when the document is printed or you use print preview.

You can force updates at other times using macros but then the user has to be willing to allow use of macros.
 

5. Of course, I use OneDrive but also save a copy on my laptop. How does that affect the filename and path?

A document on OneDrive and on your computer will have different paths because they are in different locations. Whether that will be shown by the field depends on how whether it is updated.

 

See also: How to insert the filename and path on the last page of a document, such that it will be updated automatically if the filename or path changes by Bill Coan, MVP.