Not really my area of expertise, but I can guide you on the first few...

1/ What is the model bringing him that money? I.e advertisement money is payed per download or per click,.. etc...

My guess would be that only the creator and his advertising provider can answer that question, however, advertising typically pays per click, or per impression (i.e. unique individual viewing the ad for a pre-determined period of time).

2/ How is advertisement displayed? E.g does advertisement pops up in the middle of the game or what else?

Flappy Bird is a game where you die often (as in, every fe seconds). The ads are displayed on the splash screen, which appears on launch, and also every time you die.

3/ How advertisement money is calculated? E.g a cent for a download or a cent if banner is clicked,.. etc

Loosely, yes, it is payment per click and/or impression. However, we are dealing with fractional cents here - values I have seen tend to place revenue is the 0.003¢ per impressions range.