Abusé literally means "abused" or "taken advantage of." However, in modern French slang, it's often used to mean "excessive," "over the top," or "ridiculous" in a negative way.
In the context of the song, when Christine and the Queens sing "C'est évident, abusé," they're likely using it in this slang sense to express that a situation is clearly unfair or outrageous, rather than implying physical abuse. It adds a contemporary, colloquial feel to the lyrics.
Five dollars changes hands over and over here, and it means something different each time. In the first verse the money is a consolation prize handed to someone who has declared hostilities — "Tu disais que c'est la guerre" (You said it's war) — and the reply is simply "Je te donne 5 dols, baby blues, 5 dols, baby" (I give you 5 dols, baby blues, 5 dols, baby). By the chorus the same note has turned into a weapon: "Donne-leur tort avec tes 5 dols" (Prove them wrong with your 5 dols), sung to someone the crowd thinks it has finished off — "Quand ils croient t'avoir mise à terre" (When they think they've put you down).
Then the bargaining turns around. "J'ai mis le genou à terre" (I got down on one knee) and "Dis moi donc ce que je dois faire?" (So tell me what should I do?) put the singer in the position she was buying her way out of, until she is the one holding out a hand: "Tiens, jette-moi 5 dols" (Here, throw me 5 dols). The invented word "dols" is worth noticing — it is the French half of a song Christine and the Queens recorded twice for the album Chris, once in French as "5 dols" and once in English as "5 dollars".