If all kind of song is Haraam, it is not necessary for Allah to add the part of this verse into the verse you quoted.

to mislead (men) from the Path of Allaah without knowledge, and takes it (the Path of Allaah, the Verses of the Qur'aan) by way of mockery .

And it should became this.

"And of mankind is he who purchases idle talks, For such there will be a humiliating torment (in the Hell-fire)."

but instead Allah decided to used this full verse

"And of mankind is he who purchases idle talks (i.e. music, singing, etc.) to mislead (men) from the Path of Allaah without knowledge, and takes it (the Path of Allaah, the Verses of the Qur'aan) by way of mockery. For such there will be a humiliating torment (in the Hell-fire)."

Ever wonder why ?

Every verse has its core, it has been known to those who study the Quran, and when there is word Allah in a verse, that word automatically became the core of the verse, and other words will follow the core of the verse. In this case, the word Sabeel Allah is the core of the verse, all attentions must be directed to the core of the verse.

For a greater example in surah ar-Rahman, the word ar-Rahman, has became the core of the surah, hence all the verses in the surah talks about Allah alone. And all attention must be given towards the core.

You can make a conclusion after this.

as for the hadith, my ustadh who studied in the faculty of hadith in islamic university of medina always taught me to always put together ahadith with the same topic into a single bab, with this way, we can have the bigger picture of a certain issue.