On a song-by-song basis, this format is often used1:
Lyrics by Dean Eikmann, Music by Dorothy Page
or, if one person composed both:
Music & Lyrics by Theresa Jones
So, if your singer/songwriter is Dave Brown, you could use:
Music & Lyrics by Dave Brown
as the first heading, and
Music by Dave Brown
as the other. You could also add a third heading:
Performed by Dave Brown
in the case where he may have performed songs that were written and composed by others.
1Examples of this format can be found here and here. Moreover, this page list several songs in both formats, along with songs that were performed by another artist, such as: "The Way We Were" Lyrics by Alan Bergman & Marilyn Bergman, Music by Marvin Hamlisch, performed by Barbra Streisand.
In the context of the sort of use that your question focuses on, the verb take functions as a so-called "light verb", "semantically weak verb" or "delexical verb". In other words, it is a kind of placeholder verb, a mere vehicle for transporting the semantically important content, namely pee, piss and so on.
As far as I can see, the kind of sense cited at point 7.a. in your list is the relevant one here.
Best Answer
To take it from from a linguistic boffin's standpoint, I guess that "older" is a deictic word: its meaning varies depending on usage. There's a handy illustration at Wikipedia's page for deixis. When you say "my older brother" you put yourself in the deictic centre. Your listener then should figure out the position of your brother relative to that centre.
As WS2 rightfully pointed out, you may with a degree of certainty say "he's my older brother" to an acquaintance who knows that you're the oldest of the flock, but not to just any John Doe.
That's because deictic words require contextual information to be fully understood, and your acquaintance will know that while you're at the deictic centre there's no way for you brother to be at the.. er.. deictic "above", because there's a.. hm.. "deictic ceiling" of the fact of your being the oldest.