What does "mayhem" mean? Some sort of a crisis or chaos?

What's "on earth" mean? In what context can I use this?

"On earth" is used in a question form to create emphasis. It's like it exaggerates what's being asked by using the size of the earth and everything in it in relation to something or someone. So you can use it when you want to create dramatic emphasis in a question form. Ex: What on earth is a cat doing in my apartment? I'm allergic to cats! Ex: Who on earth is that? I LOVE their outfit. Ex: Why on earth would I believe you?

What's "pass through" mean?

To "pass through" means to stop at or visit a place for only a short time. The lyrics "just passin' through" express that the singer doesn't intend to stay, he is only there temporarily. Ex: I'm passing through several different towns on my road trip. Ex: She had a summer fling with a backpacker that was passing through her town.

What's "scam for" mean? Is this a phrasal verb?

To "scam for [something]" means to trick or "swindle" someone to get something. This isn't a phrasal verb! The preposition "for" indicates the purpose of the "scamming" here. Although, I wouldn't say it's common to scam someone for "books," usually it's for money or something valuable. Ex: They scammed him for everything he had. Left him penniless. Ex: I've heard scammers are now scamming people by luring them with Bitcoin.

Why "way" is used in here? I think it is okay even though if it is not in here.

Yes, you're right. 'Way' in this case is used as an adverb meaning "a lot". Ex: I was way ahead of him.

What's "down-on-your-luck" mean?

The phrase "down on your luck" means experiencing a bad situation or having almost no money. Here, it's used as an adjective, which is why it's completely hyphenated! Ex: I don't enjoy watching these down-on-your-luck TV shows. I prefer happy, light-hearted shows. Ex: She's been down on her luck recently. Ex: Charlie has been down on his luck for a couple of years now. He still hasn't found a stable job.