I run an old version of Android, but in theory you should be able to long-press it (maybe 5 seconds) and move it to a "remove" location. Failing that, there should be a setting to remove it.
No. And my Android has never respected my search engine choice. I don't understand why people are acting like there is something wrong with us a customers. I have a CS degree. Why can't I choose a search engine? Also the "news" that Google shows me by spying on the very few searches I have accidentally been tricked into Googling are often clickbait and factually incorrect.
On old versions of Android, the search bar was a simple home screen widget, which you could add and remove like any other home screen widget. On newer versions of Android, however, the search bar is part of the default launcher, so the only way to remove it is to switch to another launcher.