or is it an error?

the previous owner built kind of a ragtag fence around the front yard.
it's about 260 ft. of fence.

the fence is built with 4x4 posts set into concrete, probably done in
the early 1970's. the rails are 2x4" (double). the fence pickets are 3'
tall, 1/4" x 1" W. very thin--most are broken or missing. some of the
rails are mounted flat, some vertical--not sure why. many of the flatted
rails have bowed terribly and come loose from the posts (no brackets,
all simple nailed).

questions:

my plan is to replace the loose posts (about 3 out of 30 are slightly
loose) then add new fence rails where they have bowed, hang all fence
rails vertically, use brackets on the ends (rather than just nails), and
use 7-1/2"x3/4"x3' cedar pickets as fill, with some space inbetween.

the 4x4x4ft. posts have 32" above ground and are spaced at 10'. from
what i have read, most people space at 8' or less.

comments? my biggest concern is whether or not i should respace the
posts down to 8 ft.

am in california desert in very stable, dry clay soil.