Would it rhyme with “may-jew” or 'my-jew"? Wikipedia isn’t helpful.
My-jew. -ai is always pronounced as eye, as far as i’m aware. Though no doubt someone will be in shortly to provide counterexamples. 
Closer to “my jew” – it would be three syllables, ka-i-ju.
My-jew, ky-jew.
And no, RT, I’m not actually sure there are, although I’m far from the most fluent Japanese speaker here. Compared to English, the correlation between written (or at least kana and romaji) and spoken Japanese is remarkably consistent.
Although I’m sure the Thinker is pretty monsterous, I believe you mean Rodan.
removed
As soon as I remember where I put my enemies list, and find a pin, and locate someplace comfortable to sit down while I write, and order a cup of coffee to drink while writing, you’re going on the enemeies list.
Perhaps he was speaking of Japanese pronunciation, rather than English.
That’s why I deleted my post, as I realized it ws stupid. I wanted to reply to yours so it’s clear to everyone that you’re not making up quoted material.
I was meaning Japanese pronounciation, but OTOH I got to learn what caisson and faience mean, so it’s win-win.
Only if you’re being excruciatingly precice with your pronunciation, or trying to fit it to a musical/poetic meter. In normal speech, the ka and i would slur into a dipthong.
You’re right, of course – I guess I was only trying to explain where the diphthong sound was coming from, i.e., from the two separate vowels “a” and “i”. English is very confusing with its spellings of diphthongs, as Skald the Rhymer’s post suggests, and the most common pronunciation of “ai” or “ay” in English, that in “daily” or “day”, would be treated as “ei” in Japanese.
IME when Japanese speakers are, for example, emphasizing words, they actually separate out things like this ka and the i into two syllables. I don’t say this means the word “really” always has two syllables, but I do think it must “feel” to a native speaker less like a single vowel sound than does the similar sound in English to a native English speaker.
Totally scientific approach, that.
-FrL-