You can render HTML content with a custom rendering engine - for example ePub ebooks are essentially bundled HTML + CSS content - there are several HTML rendering engines that read ePub ebooks but don't use Webkit.
Also, you can build a UI using web languages and render to native controls, all without using WebKit if you'd like.
No, they must use WebKit:
"Apps that browse the web must use the iOS WebKit framework and WebKit Javascript"
https://developer.apple.com/app-store/review/guidelines/