This is the second time in this lesson the audio for "menu" sounds like "meni". Is that wrong, or is there some rule I'm missing?
Hm, a bit strange to me as in French it's actually like "menü" and not "meni"
Well, seems that our nation's French isn't that great. That's why mihxal called it "French-like" :D
Somewhat true. But the sound I actually was talking about is not an "u" but rather like the German "ü". In German the word "Menü" is pronounced same as in French. The transcription on your link denotes it as [məny]. It's the same sound as in other French words like "tu", "rue", "avenue", "unique" etc.
Yes, in principle like in "fünf". To me "ü" and Polish "y" (Russian "ы") are totally different :) In your last link for /y/ the text says: "Across many languages, it is most commonly represented orthographically as ⟨ü⟩ (in German, Turkish and Basque)" And if you scroll down on the page, there is an example in German: "über". That's exactly that sound.
And just to clarify: I have no problem with the fact that Polish pronounces the word a bit differently than one would expect it. Never mind! :-)