Can the user set privacy to single fields of a field group?

No, privacy would need to be on the entire field group field.

1) can I set this to the top of the entry ist?

Move the privacy selector? No, it's always inserted where field icons are inserted so it's always after the field. You may want to consider using Simple privacy mode which consolidates privacy selection under a single Privacy tab. See my below blog post regarding this feature.

www.joomlapolis.com/blog/kyle/18860-cb-privacy-6-1-0

2) can I add in the profile view (not ajax editing) an info like "This content is visible for "privacy group" that is only visible for the user, so that he knows easily what he has set for this content (without editing view of the content)?

Yes, use the "Display Override" parameter in the privacy settings of the field. You can have it display whatever you like.

But what, if he want to delete this frist entry, so that nothing is shown anymore? I have most of the field set to require, so he cannot make all fields empty, but even this won't help.

Don't set the fields required if they're optional. There's no functionality to not have a set of fields as it'd just be too confusing for users to use.

I ment the own profile view, so only what the user see of his own profile. He has the pencil shown to edit the tabs with the group fields. What privacy is set he cannot see here. He must edit the tab and then he has the select option.

Add privacy controls to the individual fields and they'll be able to see the privacy value they selected when editing the field in ajax. There is no tab ajax editing at this time so they won't be able to see tab privacy anywhere except profile edit.

My question is, how I can add a hint about the current privacy setting of the different group fields in the own profile view for the user, what is seen only by the user itself. Is there a possibility in CB?

There's no functionality for such an indicator and there are currently no plans to implement one.

Addition: may be a link to the public view of the profile would do it also, so the user can check easily how his profile is seen in public (without log off), is this possible?

Viewing your profile as someone else (e.g. public) like Facebook is not implemented. This maybe something we implement in a future release once profile has been redesigned to have 2 views (your Home page and your Profile page; similar to Facebook and other social networks). The redesign plan is after we begin using Symfony so we can redesign everything using Twig templates. So likely won't be until mid-next year that we completely redo the profile design.