Does UIWebView use the same JavaScript engine as Mobile Safari?
UIWebView does not have the Nitro Javascript engine, so it executes JS slower than Mobile Safari. So it's not the same.
Also, does UIWebView support all HTML5 features like Mobile Safari does? I am specifically concerned about Web SQL and Web Workers
Not sure about this one. Probably not. At least UIWebView is a bit more strict than Safari on certain features. Example: when setting a width/height style through JS, you need to add 'px' behind the number, while Mobile Safari does not require that.
If I have an app which is written purely in HTML and JS, should I wrap it up in a UIWebView or should I have it open in Mobile Safari
If you want to release the app on the App Store, you will have to wrap it. If not, you don't really have to.
Are pure HTML and JS apps accepted on the Apple store?
If you wrap it, yes. But it has some limitations, as James Webster wrote.
See this question here on SO for more information on the differences between UIWebView and Safari.
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