Hi, no you shouldn't remove information_schema, I don't think you can even delete that; it's there by default. Also, when you click remove, did you check the box that says 'Check this box if you also want to remove the published website folder.' That's the reason the website is still there, that box needs to be checked. Sorry, you only need to delete the tables in the database if you had a user login system on your site then you would have had to remove it. But, now that you have deleted the folders, it doesn't really matter. Now, you can add whatever you want.
Thank You