Note that Google Chrome was previously available with a "Metro app version" during Win 8 but they retired it.
Google will release one if they expect a market share for Windows S. They are offering the browser as a gateway to their services after all.
Yup. Same for the Firefox version. Both can do it, but as long as almost everyone on Windows can support the standard Win32 version and a large number can't use the UWP version, it makes no sense to expend a lot of effort on this.
IIRC browsers in Win 8 "Metro" mode had some exceptions, like they could run non-Metro code in the background. This time around they don't seem to be offering this exception.