I don't know what your talking about (hiding post, widgets), your answer to If Google can see the text is by looking at the Google Cache (text version). If you see the text in the cache (text version), Google can see the same text.

I am not 100% what you're asking but you can ask search engines not to index your website in Wordpress but it is not guaranteed that it will work.

Once your pages are indexed it might be difficult to get them off search engines unless you take your website down altogether for awhile.

There are also plugins that can help you make a post noindex, nofollow and it will make it so search engines don't index it.

You can remove the related posts widget. It's fine. It's not against the rules. Google doesn't care. Google will still find your posts.