Regarding your size issue:
Is there a size of your tabs in which 80-90% of the labels fit? If so I would suggest using that size as your default. And for bigger tabs you could make them grow according to content. That way you will have a good solution for most of your users and still be able to accomodate those select few that have bigger names for the tabs.
Regarding the distinction of tab and content:
It really comes down to the graphic design. As some of the other commenters pointed out, letting the background colors of the tabs flow over in the document is most commonly used to provide a visual indication. Here's an example of your mockup:
However there are alternatives which could suit your problem better. Below are some examples from Outlook, but there are plenty around to choose from.
Normal use of tabs, applied in the microsoft Ribbon. Notice the different color of the 'Bestand' (File) menu to make clear that it is a key tab
Tabbed navigation menu. Notice the different way of visualizing the link between the content and the tab item.
- Tab List: This is a good way of handling a large amount of tabs (5+) because if you get too many tabbed pages to display in one row you should either reconsider the amount of tabs or start using a list like this.
Hope this helps you get some ideas about how to handle your design problem