Is there any chance the music section is legal? I would love to be able to put songs on my own pages, but I assumed it would be a legal issue? Is there a way to license songs at a reasonable price.
If you're specific question was meant to be "did this person license this music legally for his site?" - yes, there's a chance he did. There's a chance he didn't. You'd have to ask him. Even if he did, that doesn't give anyone else rights to use those songs on their site.
which has three somewhat popular songs,
making royalty-free music emphatically not the topic.
Incredibly unlikely.
"Dance Yrself Clean" is owned by Warner Music Group, "Come On Eileen" is owned by Universal Music Group.
Both are highly litigious, extremely rights-protective and not in the habit of licensing music for free.
It is far more likely the person who put the site up just YOLO'd it and is hoping they never notice.