Unfortunately, unlike WordPress or any other CMS, Q2A HTML structure written inline with PHP ( I pointed this few times before ) and so you have to dig into PHP anyway to find actual structure if you want to modify anything within the structure.
I think you do not need many things to change as per your layout but most part can be done wtih CSS. However as your layout is very basic so it is also depend what graphical elements you want to implement.
In fact you can find all HTML in qa-include/qa-theme-base.php file. Everything related theme you will find there and follow this guide to built your own theme.http://question2answer.org/themes.php
You may or maynot require PHP knowledge depending on the level of customization you want to do. However most of the part you can just only include and replace withing the class and it works in major part.
Ask box is a widget and you can place in defined paces without touching any code. However if you want to change default location than you may have to alter/modify default location for the widget area. Which also you will find in the above theme base php file.
All in above if you have some knowledge of PHP that will helps you more than just HTML and CSS of course.