I have a problem forming the correct singular and plural forms of adjective nouns, e.g. (the) old(s), her young(s), (the) red(s), (the) relative(s), (the) saint(s), (the) possible(s), (the) sick(s). Could someone explain or recommend an article?
Two of your examples are not adjectives used as nouns, but simply nouns: "saint" and "relative".
"Saint" is never an adjective. The adjective form is "saintly".
"Relative" is a word with at least two definitions. It can be used as an adjective meaning "considered in comparison to something else". Like, "Bob's house is large relative to my house." But this use is rarely if ever used as a noun. It can also be a noun meaning "a member of a family", like, "My living relatives include my mother and 3 brothers."
But that said ...
Most of the other examples you give are used as collective nouns. For example, we say, "The sick need a doctor", meaning, "Sick people need a doctor." In such cases we use the word "the" followed by the singular form. "The sick ...", "the young ...", "the possible ...", etc.
The only exception I see among your example is "red". If I was talking about some objects that come in literal different colors, pieces of some kind of candy perhaps, I'd probably say, "I like the reds best", not "the red". Similarly, if we're talking about communists, we sometimes call them "the Reds". Frankly I'm not sure why this is different. I'll gladly yield to someone who can explain this special case.