He pronounces it Mee-ka, and he actually changed it from Mica because he said people kept getting it wrong. (I guess they were calling him My-ka, maybe?)
Oh! On the subject of his privacy and all the other speculations related to that: there's an interview with him here, where he is asked to tell the background info on some of his songs. There is one song out of the batch that, according to the interviewer, Mika did not want to discuss ("Mika wanted the story of this song kept a secret").
It is pretty obvious why, because it is about family issues that I should think he wouldn't exactly like to air beyond what's already in the lyrics. But, here is a sample of some of the lyrics:
Oh, oh, oh - Is there anybody home?
Who will believe me, won't deceive me, won't try to change me?
I look at you,
You look at me,
We bite each other.
And with your bitter words you kick me in the gutter.
Ours is a family that's based upon tradition
But with my careless words I tread upon your vision.
This is who I am,
This ain't a greater plan to break your heart of me.
Ah, ah, ah - Is there anybody home?
Who wants to have me, just to love me?
It could easily be about something else entirely, of course, but still.