Hi,
To remove the /index.php/ part from the URL you need to enable the Use URL rewriting option in Joomla's Global Configuration.
JoomSEF supports only the core Joomla components by default, so you would need to install the Joomanager extension for JoomSEF to get nice SEF URLs. We currently don't offer an extension for it, but as a paid service we could implement it for you.
The missing CSS is probably caused by relative URLs being used in CSS stylesheets definition. Either change the CSS links in your template to absolute form (starting with slash or including the domain) or open JoomSEF's Configuration, make sure that Professional mode is enabled, and then on the Advanced tab set "Set page base href" option to "Yes - always use only base URL".
We only offer our free support through our forums, if you want us to check your website's configuration directly, it's a paid support service:
www.artio.net/e-shop/support-services