page-server: Split the code doing async page-read (v2)

This is prerequisite for the next patch.

v2: spellchecks, code reshuffle

Signed-off-by: Pavel Emelyanov <xemul@virtuozzo.com>
Acked-by: Mike Rapoport <rppt@linux.vnet.ibm.com>
Signed-off-by: Andrei Vagin <avagin@virtuozzo.com>