You could add the delays and fade-outs at the same time, like this DEMO:
$(document).ready(function () {
$('#h2-1').delay(1000).fadeIn(2000).delay(2000).fadeOut(2000);
$('#p-1').delay(3000).fadeIn(2000).fadeOut(2000);
$('#h2-2').delay(8000).fadeIn(2000).delay(2000).fadeOut(2000);
$('#p-2').delay(10000).fadeIn(2000).fadeOut(2000);
});
Also, if you want them to fade in from the start, they should be hidden from the start. I've added style="display:none;"
to all elements in the fiddle, but you could handle it with jQuery as well.