Ajax Call in page theme not working?

  1. You shouldn’t be including jQuery explicitly. WP ships with a copy and multiple copies tend to mess things up. See wp_enqueue_script().

  2. You shouldn’t be trying to load PHP file inside a theme directly. It won’t load WordPress environment that way (unless it tries to do so explicitly, which is usually very fragile and pretty much cannot be reliably done in public code).

  3. Error 500 is unfortunately very not transparent thing. It is produced by your web server rather than WordPress and there is no insight into what might be causing it that can be gained on WP level. You’ll have to look up details for error in your web server logs / ask hosting support to do that.