You can record any song that has already been recorded and published. You need what is called a "mechanical license," which is inexpensive and cannot be denied. The lyrics are part of the copyrighted work.
Yeah, that's specifically and only for recording a "cover" of a "published" [which in the music biz means released by a major label, or did not too long ago, but these things can change] song, and ONLY that. If you use the lyrics as part of a written work, that's different, and has nothing to do with mechanical royalties. There's a lot of twisty passages in copyright law.
There are so-called "fair use" provisions in copyright law that permit the use of fragments of copyrighted works, but your use has to qualify under those provisions.
If I wrote:
I walked to the door singing, "Fly me to the moon,"
It cannot be determined whether I am quoting the lyrics or the title. If, however, I follow that up with, "Let me play among the stars," I am definitely quoting lyrics and would need permission. Typically the copyright holder wants to be acknowledged in the front matter.[/QUOTE]
Unfortunately, "Fair Use" is whatever a judge rules it is in any particular case. Song lyrics are so short that (apparently from rulings by judges) use of ANY lyric long enough to be recognized as part of the song is too much to be covered by fair use, and rights holders sue over such "minor" uses of lyrics.
There's a lot of writings on copyright law at
http://copyright.gov and amazingly, most of it is in plain and easily (relative to how complicated the law is) read English. But you pretty much have to read it all, because laws in one area (such as printed word) are very different from other areas (music lyrics, musical compositions, music recordings, movies, digital encodings of these things, whatever else) and using works or excerpts of something from any of these areas in any other area.
I don't want to sound rude here, but you're wrong. In fiction, anything in quotes is dialogue. As first quoted, as well as in your quote, he is singing the words of the song no matter what he follows it up with.
Now, if it were, George walked to the door singing Fly me to the Moon, that would be telling he is singing the song, not showing via dialogue.
Do you have a reference for that? I've not heard of the "dialogue" distinction before.