StaffGroup question

[Jeffery B. Rancier]

Why in the following example does 'lower' staff inherit the time
signature property, but not the key signature?  And is this the right
place to set them?  (This is from the satb.ly template?)  And is 's1'
just a name holder to associate each Lyrics and Staff contexts with
each other?

,----
| \score
| {
|     \notes
|     \context StaffGroup
|     <
|       \property Score.automaticMelismata = ##t
|       
|       \context Lyrics = tenorLyrs { s1 }
|       \context Staff = upper {\time 2/2 \key ef\major s1 }
|       \context Lyrics = leadLyrs { s1 }
|       \context Lyrics = bariLyrs { s1 }
|       \context Staff = lower {\clef bass s1 }
|       \context Lyrics = bassLyrs { s1 }
| 
|       \addlyrics
|       \context Staff = upper \context Voice = VA { \voiceOne \tenorMusic }
|       \context Lyrics = tenorLyrs { \tenorWords}
|       \addlyrics
|       \context Staff = upper \context Voice = VB { \voiceTwo \leadMusic }
|       \context Lyrics = leadLyrs { \leadWords}
|       \addlyrics
|       \context Staff = lower \context Voice = VA { \voiceOne \bariMusic }
|       \context Lyrics = bariLyrs { \bariWords}
|       \addlyrics
|       \context Staff = lower  \context Voice = VB { \voiceTwo \bassMusic }
|       \context Lyrics = bassLyrs { \bassWords}
|     >
|     \include "../../templates/paper.ly"
|     \include "../../templates/midi.ly"
| }
`----

-- 
Thanks,
Jeff