The phrase "free storage" is used to refer to available unused storage.

Can we use the phrase "gratis storage" or "complimentary storage" to refer to storage for which money is not being charged.

This should make searches for either topic more precise.

El pajaro es libre
The bird is free

Perritos Calientes gratis!
Free Hot Dogs!

Free speech, free beer and free software...

Free software is a matter of liberty, not price. To understand the concept, you should think of free as in free speech, not as in free beer.