You can control whether a Public Install Page should be available for the given app artifact with the Deploy to Bitrise.io step’s Enable public page for the App? input. If enabled it will enable the Public Install Page for the specific app artifact it uploads - you can also enable & disable a public page after that on the Build’s page. There’s only one exception, AppStore signed iOS apps (ipa) - those can’t have Public Install Page because you can’t install an AppStore signed iOS app from anywhere else except from the AppStore and from iTunes Connect TestFlight.
The URL of the public install page is permanent, but that given URL will always point to the same version / same artifact, not to the latest version.
Enterprise works as expected, only AppStore signed iOS apps can’t have a Public Install Page.
A given link does not change, but every build will generate a new URL for the new app artifact. Previous URLs will still work, but will point to the previous versions, not to the latest version.
Currently there’s no single URL to get the latest version of an artifact, if you’d need that feel free to vote & comment on the related Feature Requests :