Recently I came across the word 狭める, "to narrow" or "to make narrow." I wondered about its relation to 狭い and then I found some other similar adjective-verb pairs:
I'm curious if this is a common way to turn adjectives (it seems like only い-adjectives) into verbs. Also, is it an alternative to the adverbial form + なる and the adverbial form + する？
It seems that only a small subset of い-adjectives can be turned into verbs by using suffixes -まる and -める.
-める generates a transitive verb and -まる an intransitive verb.
So, for a single い-adjective, both -める and -まる verbs may exist:
For some い-adjectives, only -める verbs are valid:
And there are many い-adjectives that do not have -まる/-める verbs.
As you mentioned, it is almost equivalent in meaning to 〜くする and 〜くなる respectively. For example, 深まる≒深くなる and 深める≒深くする. But they are not always interchangeable and their usage may be difficult, as described in this article.
This book is describing the differences between -まる/-める verbs and -くなる/-くする in p.401:
「〜くなる」「〜くする」は形容詞の表す程度がより甚だしくなる（する）ことを表しますが、「〜まる」「〜める」は形容詞の表す状態への変化を表します。ただし厳密には区別されない場合もあります。
It is indeed a common way to turn adjectives into verbs.
But such a rule is not universal, there are many exceptions.
Not all verbs ending in まる or める are derived from adjectives.
And not all adjectives can be turned into verbs using this rule.
For example the following verbs are probably not derived from adjectives:
決める
含める
埋める
The following adjectives don't have a corresponding verb:
安い
痒い
白い
