I blocked one Facebook page but I still see it on my News Feed from my friends' shared status. Is there any way I can block this page totally?
You have already blocked that page totally, what you are seeing is your friend's activity not page's activity. What you are looking, for that you have to block your friends who is sharing that page's activity. There is no other way (atleast I didn't find).
Once you block a Page, that Page can no longer interact with your posts or like or reply to your comments. You won't be able to post on the Page or message the Page. If you like the Page, you'll unlike and unfollow it.