Hello!
In all examples that ralated to find and cpio find is always used with currect folder . :

But why? Is any troubles if I will specify something like /home/user as a find argument?

You asked the same question over on the Fedora forums. I'll give the same answer here:

You embed the full path into the archive.

This can make it more problematical when you try to extract a single file - with the full path embedded it has to go back to exactly where it was, which doesn't work if the files are to be restored to a different username on a different system.

It isn't a problem if that is exactly what you want to do - every time.

Most such extractions I have done though, require the extracted file to be separate - it may be because I need to do a diff between the backed up file, and the current file.

This happens so often that tar even removes the leading "/" to make such use possible even with the full path specified. You can override tars removal, but it saves time.
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Here are some examples where they have used find with cpio to take back up but they did not use . (current directory) they have used absolute path.
http://www.cyberciti.biz/faq/how-do-...d-under-linux/
http://http418.net/copying-stuff-with-find-and-cpio/