Learn French: Il a affirmé que le camion avait reculé dans son pare-chocs. - He stated that the truck had backed into his bumper.

This is the rule of sequence of tenses in reported speech. The main verb (a affirmé) is in the past. If his original words were in the Passé Composé ("The truck backed up" / "Le camion a reculé"), the reported version must take a step further back in time to the Plus-que-parfait (avait reculé) to show the action happened before he made his statement.

Why is the preposition dans used to mean "into"?

While dans usually translates to "in", French often uses it after verbs of motion like reculer (to reverse) or rentrer (to crash/enter) to express colliding with or going into something. You can think of it as the truck reversing "in" the space occupied by the bumper.

Why does pare-chocs end with an "s" if it's just a single bumper?

Pare-chocs is a compound noun made of the verb parer (to ward off) and the noun chocs (impacts/shocks). It literally translates to an "impact-protector." Because a bumper is designed to protect against multiple impacts, chocs keeps its plural "s" even when you are only talking about one bumper (un pare-chocs).

Could I just use a dit (said) instead of a affirmé (stated)?