The policy used to exist, it was Section 3.3.1 of the iOS Developer Agreement in 2010 [1]:

"Applications must be originally written in Objective-C, C, C++, or JavaScript as executed by the iPhone OS WebKit engine, and only code written in C, C++, and Objective-C may compile and directly link against the Documented APIs"

Steve Jobs also wrote some emails on the issue [2], but by September 2010 and following a potential Federal Trade Commission investigation, the clause had been removed again [3].

[1] https://daringfireball.net/2010/04/iphone_agreement_bans_fla...

[2] https://www.taoeffect.com/blog/2010/04/steve-jobs-response-o...

[3] http://www.peterfriese.de/apples-updated-developer-license-t...

No, Apple does not allow JIT. It does not dictate language use.

I did actually think that Apple required the use of Apple's developer tools for iThing apps --- so unless you can compile your target language into C, C++, ObjC (or Swift, I suppose) and then use XCode to compile the final binary, your app would be rejected. Has this changed?

There are plenty of apps on the App Store with using Flash (Adobe AiR). As well as other languages like JS (React Native, Titanium).

I think you're thinking of when iOS decided not to support Flash in the browser.