Oracle sleep func in Apex

APEX_UTIL.PAUSE(5); --sleep for 5 second

Setting Session State with PL/SQL

APEX_UTIL.set_session_state(p_name => 'PX_MY_ITEM', p_value => 'wibble');

Implement a busy modal indicator in Oracle Apex

At the start of your processing, execute (javascript):

    apex.widget.waitPopup()

And when done, just remove the elements (again, javascript): 

    $(".u-Processing,#apex_wait_overlay").remove();