These are both examples of computer programming lingo that someone living a few decades ago may have thought were strange but are common in modern English.
On screen is an idiomatic phrase that came about with the rise of computers. For clarity, we might even write it "on-screen." There isn't a general rule for why this came about that I know of. There are a number of such special phrases in English (where no article is used). You may just need to learn them.
White-space is also idiomatic jargon, but it's a little easier to explain. "A white space" would mean one empty character. White space may or may not be countable (either a certain number of spaces and tabs or an amount of white space). When we say "white space" the word "space" does not refer to a single character, but a generic area of emptiness, which may be filled with either spaces, tabs, or something else.
To see it more clearly, remove the "white."
Space is free.
Makes perfect sense. It refers to an empty area of indeterminate size.
A space is free.
In computers this refers to a single space character.
The author you have referenced indicates that white space, whether made up of a bunch of spaces or tabs or one space, is always free.