Also, what do you mean by
Put your database connection script outside the area where it can be directly accessed by a browser (below the level of public_html directory if possible).
?
Maybe it's a shame but I don't have a public_html folder. All my php projects are stored in the root of the server : the www folder.
On a web server the doccuments are stored in the www folder, typically on a live installation of a site you would never normally store a connection script in that folder, instead you should store it outside that directory and access it like;
require_once ('../somedir/mysql_live_connect.php');
Because regardless of what you think, there are some means where scripts can be viewed in a browser, storing it outside the www or public_html directory makes it inaccessible to people who would try and access it in your browser.
Other things about mysql injection, if I was to try and hack a website that used a mysql database then the way I would first try and do this would be by trying to supply it with an invalid query to cause an error and thereby try to reveal something about the database.
Typically this could be done by cross site scripting, I would write a script on my own server which would call one of your php scripts, if you have a form in your page it is easy to see which script it actions when you click submit so my form would just call the same script, furthermore I would know the variable names in your form from the HTML, I could pass my own values into these variables and try to escape your sql query string (i am not going to post this in public) and add my own commands to the sql query.
SQL injection is something you should take very seriously, preferably you should use prepared statements, at the very least use mysqli_real_escape_string, htmlentities converts any html tags eg; < to < etc to prevent the kind of javascript thing I did, striptags is another good function to remove potentially harmful code.
Finally I am kind of sad that you took the site down, it was looking good.