Not Chrome, because it is so tightly integrated with the system. But you can change to Bing or use Word Online instead of Google Docs.

You can't install apps from outside Google Play (for Chromebooks that can run Android apps) or Chrome Web Store. But you can unlock it (developer mode) and get basically a Gentoo with a custom display server and desktop environment.

The admins can lock your options down and apply a lot of surveillance too.

I don't think this is apples to apples, because ChromeOS tries as best it can to make the browser the entire OS, with any remaining Linux components abstracted away. So I wouldn't necessarily consider it anti-competitive that a Chromebook can only run Chrome, anymore than I would it consider anti-competitive that a Nintendo Switch can only run Nintendo Switch games.

But to strictly answer your question, the Chromebook does allow you to turn on developer mode, where you could then install a Debian/Ubuntu chroot via crouton, on which you could then install Firefox. So in a word, yes.

It does let you use Bing and office 365.

You can install any Android browser on Chrome OS devices that are capable of running Android apps e.g. Firefox.

That's not a fair comparison. That's like asking if Windows allows you to not use Windows.

Chrome let's you use arbitrary apps not selected by Google; web apps. These apps are first class citizens in the UI with all of the same OS access as Google's apps.

That's like asking does Chrome browser allow you to run Safari or Edge.

And with the play store coming it allows you to install other browsers like firefox.

Does ChromeOS allow you to change the search engine? Yes.

Does Windows 10 S allow you to change the search engine? No.