btw: yesterday I tried to update the theme and broke my website... It's now update correctly...
One major problem I see is that it appears you're using Thematic and the theme has been modified directly.
If you intend on moving forward with customizing a theme that is distributed by WordPress, you should probably change the name of the theme in the style.css. This will protect your client or some future developer from upgrading theme, which will overwrite any and all the modifications to the theme.
It's unfortunate for the site owner if this is the case. They are boxed into a corner by an outdated theme that uses deprecated functions. The theme will eventually fail to work with WordPress and there are security implications as well.
Creating a child theme is the best choice when building off a publicly distributed theme. If you need more help working with Thematic you're welcome to come by ThematicTheme.com for community support and documentation.