I found a solution to my problem, or let's say a work-around.
Here the details, if someone is facing a similiar problem.
The file where all data is stored is named: "AddressBook-v22.abcddb" (at least since OSX 10.7)
It takes it's data from "Metadata" and "Images" (if ever you have pics with your contacts), locate in the same file AddressBook.
- So I closed the application AddressBook.
- I opened "AddressBook-v22.abcddb" with TextEdit and copied the first line), something like "SQLite format 3 @ Çbo H Ç-‚ ÏK ˚ ˆ Ò ÏMUIAL0J 9 9 9 9 9 : : 9 9 @ @ A A 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9"
- Deleted all files, means "AddressBook-v22.abcddb", "Metadata" and "Images".
- Then I went back with Time Machine and grabbed good/right/non-corrupted files (The same three files).
- Then I copied them in my current system (Application Support/AddressBook/here).
- Copied the original first line into "AddressBook-v22.abcddb" (Yes, the "SQLite format 3 @ Çbo H Ç-‚ ÏK ˚ ˆ Ò ÏMUIAL0J 9 9 9 9 9 : : 9 9 @ @ A A 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9"-thing).
Then I restarted the application AddressBook and - voilá - all at it's place like it should be.
iCloud data is stored in a subfile named "Sources" (located in also in Application Support/AddressBook/here). In there you find the same file tree, like on level above. And you can handle it just the same.
Happy eastern to everyone!