Why do you have a separate {...} \\ {...} for each bar?
(I agree that it might make the input more readable). Otherwise,
you can save some typing by
lower = \relative c
{
\clef bass
\key b \major
\time 6/8
{ \slurDown \override Rest #'staff-position = #2
3) The lower system has an overlay of the rest and the g. I assume
Lilypond
counts the voices from top to bottom. So I changed the order in the
second
measure. But this gives a too high rest. It should be from third to
fifths
line.
Try setting the rest manually with something like