Learn English – say “medium-term”, as with the adjectives “short-term” and “long-term”? Do they need prepositions

The Adjectives article in wikipedia mentions four kinds of use of adjectives; see the article for details, but (in brief) it refers to Attributive adjectives, Predicative adjectives, Absolute adjectives, and Nominal adjectives. In your example "This ruler is long", long is being used as a nominal adjective, in spite of being a relative term. Note, your question presupposes the adjectives in the examples are relative terms; that there is another object being compared to; but often the comparison is to a fixed set of things, and within that framework the comparison is absolute rather than relative.

Well, I think grammarians are going to have various opinions, but the Oxford English Dictionary thinks these are both nouns. Or, more precisely, they are adjectives used as "absolute" constructions which omit the noun they reference implicitly, somewhat similarly to a process where we use an adjective as a substantive, like referring to the weak when we mean the weak [people].

There are all sorts of uses in English (and other languages) where we just use AdjectiveX to mean AdjectiveX [things, people, etc.], and when such uses become idiomatic, the adjective is effectively converted into a noun. Combining such an adjective with a preposition isn't an exception in English either, though these idioms are a little unusual in that such absolute constructions often have the before the adjective to mark it as a noun.

Anyhow, here are some excerpts from the definitions and related senses in the OED.

For in brief:

n.

a. in brief: in few words, shortly, concisely. With ellipsis of ‘to speak’: In short, to sum up.

†b. the brief, used absol. like the short. Obs.

The (a) usage has an earliest citation of 1423, which is roughly the same time when "brief" first came to be used as an adjective in English. (Notably, the use of "brief" as a noun in the sense of a formal letter, dispatch, or note has citations at least a century earlier; whether there's a connection between this idiom and the slightly older noun is a question I leave to the professional etymologists. The OED seems to think "no.")

For in short:

n.

I. The neuter adj. used absol.

1. With prepositions, forming adv. phrases.

   a. in short (also Sc. †at short): briefly, concisely. From the 18th c. onwards used only as parenthetical phrase, introducing or accompanying a summary statement of what has been previously said. †in short and plain: briefly and plainly.

   †b. in short (? also Sc. at short): in a short time, quickly. Obs.

   c. for short: as an abbreviation.

2. the short: the total, the result, upshot; a brief summing up of something which has been previously explained in full. Now only dial. (Cf. the long and the short of (it, etc.) ...) †short is: ‘to speak briefly’, ‘the short of the matter is’.

3. Phr. to draw short and long : to draw lots by means of straws, etc. of different lengths.

The phrase in short and plain dates at least back to Chaucer, but the OED has the first citations of at short and in short in the first sense in the 1500s.