1. Place the book upside down on the desk.

2. Place the book face down on the desk.

3. He placed the cup upside down on the table.
4. He placed the cup face down on the table.
(Can we use both expressions together? Is each pair the same in meaning?)

1 and 2 are fine, and so is 3.

4 is not used since a cup doesn't have a "face."

Yes, in both cases, "upside down" and "face down" can be used interchangeably to mean the same thing. Both expressions describe the position of an object where the top surface is facing down or in a downward direction.

So, in the context of your examples:
1. Placing the book upside down on the desk means that the book is positioned in such a way that its front cover and pages are facing downwards, while the back cover is facing upward.
2. Placing the book face down on the desk also means that the book is positioned with the front cover and pages facing downward.

Likewise:
3. Placing the cup upside down on the table means that the cup is positioned in such a way that its opening is facing down towards the table surface.
4. Placing the cup face down on the table also means that the cup is positioned with its opening facing downward.

So, each pair of expressions has the same meaning and can be used interchangeably depending on personal preference or regional variation.