1. The tab should only show a special joomla category names Angebote

Within CB Articles > Parameters > Articles you can select what categories to exclude. You'd have to exclude all of them except your specific category.

2. If the offer is only for members it should be marked for members only, or the offers are public so i need a possiblity to select as public/member etc.

You mean you need to set the access permission for the tab per user? That should be doable using CB Privacy and enabling privacy controls for the Articles tab. If you mean permissions per article then you'd have to use Joomlas built in access functionality for that.

3. the users thats gives the offer havent any profession to write joomla articles

That'd be entirely on Joomla permissions for that. CB Articles just displays links to the articles and nothing more. So in your case you need to be sure to give users the appropriate Joomla usergroup so they've permission to create articles.

Now the question is. Can we realise with fields a mask for post in thats way? (Needed fields are: title, name, company, picture, description, upload/download, url, maybe a choice to select the usergroup,e.g. public or members)

You don't need CB fields for any of that. You'd just use Joomlas built in submit article page.

These offers should be public on members tab names offers and visible on the website on a seperated page

They'd be visible on their profile via CB Articles and visible elsewhere via normal Joomla content menu items or even Joomla article module.