How can I print a file from the command line?

Since it is a .docx-file Microsoft Word is probably the best program to do the task.

I would have a look at the [command line arguments] to Word:

Have a look at the following switches:

/q, /n, /mFilePrintDefault and /mFileExit

(/q and /n explained in the page above, and /mXxxx refers to macros. Have a look att google.)

Example:

WINWORD.EXE your_document.docx /mFilePrintDefault /mFileExit /q /n

The following page seems to explain how to convert it to PDF.