Weather app

Depends on what exactly you are trying to accomplish.

You can totally ignore the default Apple Wheater App and remove it from the Today screen. Outside of that, there's nothing that states the Weather app is the default go to place for weather for anything.

When adding the Dark sky App, you can activate its Weather Wdiget for the Today View instead of the Weather App and just place the Dark Sky app on a home screen you want the App to live in.

You can add specific shortcuts to Siri to get details from specific apps using Shortcuts. Dark sky is one of the apps that support direct shortcuts with Siri.

See here: https://ios.gadgethacks.com/how-to/use-siri-with-third-party-weather-app-instead-apples-your-iphone-0192302/

Not at this time.