Starting with Windows 10 build 17040, there is a hidden new floating Search bar that can be enabled for a more immersive Cortana that Microsoft is testing.
Windows 10 comes with a Search box and a Task View button enabled on the taskbar. They take up valuable space on the taskbar. Although they look like any other regular pinned app, they have no context menu. Windows 10 users may want to hide these controls to get more room for running apps. Here is how to get rid of the Search box and the Task View button on the taskbar.
In Windows 10, Cortana can only be integrated with Bing and Microsoft Edge. The server-side part of Cortana is locked down. You cannot change the search engine in Cortana to Google or use alternative web browsers for web links. This post explains how to Make Cortana open links in the default web browser.