If you're doing user-agent detection, your code is broken by design. Use feature detection instead.
Please. I'm tired of having to use an extension to spoof user-agent in order for some websites to work. The creators of the Vivaldi browser were even forced to permanently spoof Chrome's user-agent due to websites unrecognizing the Vivaldi one.
In general yes. In some specialty cases user agent detection is fine, e.g. if the application has critical and specific requirements on what software/hardware stack it should be ran on and has been tested for. Just because a feature has been detected to exist in the browser doesn't mean it works correctly, after all. But even in these cases, detecting a non-supported browser should throw a warning, not prevent you from accessing a site.