GA's Download code doesn't work

Question 1

There are two things that I can see in the in the site you linked that might be causing you problems The first is stated in the answer by Pablo Romeo:

you need to add onclick="code here" in order to send event when the user Clicks the link.

<a class="btn btn-inverse btn-small pull-left" href="http://www.mannachurch.org/online-video-notes/letsmove_questions_pt1.pdf" onclick="ga('send', 'event', 'Questions PDF', 'click');" target="_blank">

The second problem is the location of your Google Analytics tracking code on that page. Its at the bottom of the <body> tag you should move it so its with in the <head></head> tags

<script>
    (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
    (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
    m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
    })(window,document,'script','//www.google-analytics.com/analytics.js','ga');

    ga('create', 'UA-43995008-1', 'mannachurch.org');
    ga('send', 'pageview');
</script>

Question 2

You can't just add javascript code into the href attribute concatenated with a url.

You should probably do something like the following:

<a class="btn btn-inverse btn-small pull-left" href="http://www.mannachurch.org/online-video-notes/letsmove_questions_pt1.pdf" onclick="ga('send', 'event', 'Questions PDF', 'click');" target="_blank"><i class="icon-file"></i><strong> Part 1</strong> • (pdf)</a>

Or a more elegant way would be to use jquery instead of the onclick event.