do not include public headers as though they are local

Avoid having to use -I trickery to find public header files included as
though they are private.
do not pretend to support -rand in apps

Remove support for parsing the unused -rand option and the unused random
buffer variables.
use BIO_write instead of an unchecked write()

write() warns if its return value is unchecked. Replace with a BIO_write
like all of the surrounding code uses anyway.