CB 2.0 will be removing tabs all together. We'll be migrating to a "fields only" style, which are much more customizable. Tabs won't be gone entirely however as a "fields container" field will be available to produce the appearance of a tab, but full features of a field. At any rate much is planned and better styling is one of those plans.

Regarding connections however this is really a fault of the connections plugin. We plan to rewrite the connections system all together with CB 2.0 however. Currently we're holding off major feature implementations to afford time to work on 2.0.

As pepperstreet has shown it can be done and each tab does have its own unique selector, which can be used to accomplish your needs. Please also note CSS3 is quite readily available as all modern browsers support it. CSS3 comes with a host of extremely useful selectors.

I remember (my) a feature request to improve the field management in backend. The idea was to sort/filter by tabs. This "little change" would improve the overview and speed in fields-manager dramaticly. Is this feature still possible for CB < 2.0 ?!

Yes, sorting, filtering, searching APIs will be better designed in CB 2.0 so any backend usage can feature them. Along with APIs for copy and export/import type features. These are all "ideas" we've down on paper and preparations for implementation (CBSubs is a huge preview of what is to come to CBs core, same for GJ 2.x). I can't guarantee any of this of course as they're ideas, but we're pretty set strong on implementing them.

How would this be done, when you don´t have an assigned tab per field? Is there any other categorization like category/tag ?

Don't fully understand the question. The idea is we'd have several field types, container types, media types. Example you could create a container field for a tab that's called "Galleries" you could create a media field for Images and essentially have a custom built image gallery. It's really vague on the details as again we're still in design process, but at this point am interested in hearing user feedback in this regard. What would YOU like it to do?