Is it possible to make for example some category in Wordpress, and make all posts/pages in this category accessible by Google, but if real visitor came to this page - he will be redirected to the page where I describe - this category will be accessible only after registration in WP etc. Is it possible ? How ?
Not sure about Google, but right above the Publish/Update Page button where it says "Visibility" (click Edit) you can make it private and require visitors to register to view the page. I've never used it, but I think you can use that.
Yes, it's easy to make it accessible only for registered users, but main question with Google access, I don't know how to make it... Only one way - make separate same articles - html files, inside the articles JavaScript redirect to the blog post, so visitors with enabled JS will be automatically redirected...