One way to access WordPress core functionality outside of your WordPress directory is to use the following example;
<?php require( '../path-to-your-wordpress-install/wp-load.php' ); get_header(); // do your magic here... get_footer(); ?>
However converting HTML to WordPress shouldn't really require you to access WordPress outside of itself. Instead you want to be porting across the clients HTML into a WordPress compatible theme.
It really is project dependent when it comes to how long it will all take. I've had projects take a couple of days to those that last several weeks.
In theory you should be able to port across the existing PHP code as it stands into your template/theme files, however that's not to say you won't encounter any bugs along the way.
It does pay to survey the site in depth and to ask as many questions as you possible can or which you feel are relevant to your client to uncover any potential time-sinks!
The general process is to know Wordpress first, so you know how it works, why it works the way it does, and the general UX behind the admin side.