Learn Russian: Почему этот мальчик так плохо себя ведёт?

Себя is the reflexive pronoun meaning "oneself," and here it is in the Accusative case. In Russian, to say someone "behaves," you literally say they "lead themselves" using the verb phrase вести себя.

I learned that ведёт comes from вести, which means "to lead." How does it mean "behaving"?

You are right! Вести is a verb of motion that means "to lead" (like leading a child by the hand). However, when paired with the reflexive pronoun себя, the phrase вести себя becomes a set expression meaning "to behave." So, the boy is literally "leading himself" badly.

Could I change the word order to ведёт себя так плохо?

Absolutely. Russian word order is quite flexible. However, it is very common for short object pronouns like себя to sit right before the verb they belong to. Both так плохо себя ведёт and так плохо ведёт себя are perfectly natural.

Why is it плохо instead of плохой?

We need an adverb here because we are describing how the boy behaves (an action), not describing the boy himself as a person. Плохо is the adverb meaning "badly," whereas плохой is the adjective meaning "bad."