Learn Russian: На стене висел детский рисунок. - A child's drawing was hanging on the wall.

In Russian, new or emphasized information is usually placed at the very end of the sentence. By starting with the location (На стене) to set the scene, the sentence builds up to the 'reveal' of what was hanging there: a child's drawing. This is very common in descriptions.

I always confuse the Russian verbs for 'to hang'. Why use висел here?

Висеть describes the state of something hanging, which is what we need here since the drawing itself was in a hanging position. This is an intransitive verb, meaning it doesn't take a direct object. If you wanted to describe the action of a person hanging the picture up, you would use the transitive verb вешать or its perfective pair повесить.

Could I say рисунок ребёнка instead of using the adjective детский?

You could, and it would be understood perfectly, but using the relational adjective детский is much more natural in Russian. Russian frequently uses adjectives formed from nouns to describe who something belongs to, who made it, or what it is for, rather than relying solely on the genitive case like English often does with 'of a'.

I noticed the word рисунок ends in -ок. Does it have a fleeting vowel?