Is there some sort of special precedure I should know of, in order to make this work better?
Does OE have issues downloading php-pages?
Regarding Facebook/Twitter - I would suggest you to select the Project that partially downloaded the site, click the AutoSave button on the Internal Browser toolbar and then click Browse. Offline Explorer Pro should download missing files.
Offline Explorer Standard Edition doesn't support this feature. You may install Offline Explorer Pro using the link: