I am contemplating writing a fictional character [nerd] who speaks in a pop culture references. I appreciate this question somewhat overlaps

Referencing modern pop culture in science fiction

The concept is a period piece so I see the use of quotes dating the work as an advantage.

The character would quote single lines of pop songs, though probably not exactly. What I'm worried about is the legality of quoting copyrighted material.

Is a single line precisely quoted a copyright infringement?
What if it's approximately quoted?
What if there's a foil character who attributes the quotes?

For example, say something bad happens

A: They must be out of their brilliant minds

B: I heard that somewhere [thinks]

A: furniture

B: what?

A: [Hums tunelessly]

B: oh yeah... 1986. Peaked at 21.

A: [gapes] high five dude

Any thoughts would be appreciated.

According to this question, you'd be in trouble if you quoted entire songs, but single lines should be okay. Making the quotes approximate would ensure you don't run into any legal issues, but would also likely prevent your readers from getting the references, which would defeat the entire purpose. So only do that as a last resort, if your publisher objects to the unedited quotes.

What if there's a foil character who attributes the quotes?

I think this is a bad idea; not from a legal standpoint, but from a writing standpoint. The sample dialogue you provided seems very, very clunky, and depending on how bad the "bad thing" is, it may also come across as very jarring and out-of-place to have the characters suddenly high-fiving each other over pop-culture references.

I must confess I'm not familiar with your example song lyric, but if I was, and I had to read six lines of dialogue explaining it, it would be a bit tedious. And if I understood all your references, and you explained them every single time... it would get annoying.

If you really want to attribute all this character's quotes - or have some way of explaining them for those who don't recognise them - I'd take the approach recommended in this question and have some kind of "Acknowledgements" section at the back of your book where you can list all the songs you referenced. That way you're still attributing the lyrics without having to stop the action every five minutes while you do so.

Citing song lyrics in a novel is not fair use. You need permission to use song lyrics in a novel.

Jane Friedman cautions:

Because songs and poems are so short, it’s dangerous to use even 1 line without asking for permission, even if you think the use could be considered fair.

And Writer's Digest explains:

Song lyrics are copyrighted, which means you need permission to use them. According to our legal expert Amy Cook, there isn’t any specific law about how much you can take under fair use, but it’s common for the music industry to say you need permission for even one line of a song.

“The music industry is pretty vigilant about song lyrics,” Cook says. “This is especially true if you’re using the lyrics in a novel to progress the story or add atmosphere. If you’re a music critic reviewing a CD, you have more leeway under fair use.”