1) The only website url in this code is a reference to an outdated jquery version. You can get rid of it, if you download the code and add it to your site. I suggest using the minified one. So download this one:
http://code.jquery.com/jquery-1.8.1.min.js[
^], copy it aside to your code, and change the reference like this:
<script type="text/javascript" src="jquery-1.8.1.min.js"></script>
2) The dollar sign is the basic function of JQuery.
So: if you remove any of it, you get nothing, since this is a JQuery based code, thus you have to rewrite it to an other ajax library, or to legacy javascript. One might do this, but is is a bad idea, since you can only loose by this step, you will gain nothing at all. But if you stick to it, you have to learn both. You can start here:
http://net.tutsplus.com/tutorials/javascript-ajax/from-jquery-to-javascript-a-reference/[
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