Haha! don't worry guys, I'm not burnt.
Sure when I opened the tank initially it went "shhhhhhhhhhhhhhhhh" like when you start opening a shaken coke bottle, so I went slowly unscrewing it.
Also, as someone explained me today, there is an air valve in the cap, so most probably the 3/4 of cooling fluid missing in the tank were gone in steam because of the overpressure, or so I undertand it.
So, to update on the situation, first I have to state that Smart s*cks. Not the car
(whilst unreliable it has great qualities), but the brand. None of the common garages
(Midas, Norauto, Speedy,etc) are going to repair a Smart
(pieces are too expensives they say), so you're forced to go to the Smart center. But those brats allways start by charging 80€ for removal of the bonnet, then they charge the diagnosis between 250€ and 450€, before even talking about a repair. And they allways conclude that you have to change everything in the end. So I won't go there wathever happens...
Anyway, I have had a few friends looking at the car and testing it, and what is confirmed now is that there is a leak of some sort in the cooling system, because in less than 20 km the tank lost about 1/4 of it's capacity again.
What's unsure is, is there an hidden leak somewhere
(can't find any trace of fluids under the car) causing the overheating, or is it the overheating
(possibly induced by the broken fan) that makes the fluid temperature raise up to the point it's spitted away by the safety valve?
Tomorrow a friend will bring a battery on which we'll plug the fan on, as to understand if it's broken or if the problem comes from elsewhere. Fuses are ok btw. Then, I'm going to purge the cooling system and refill it, adding an anti-leak paste
(the problem with that is that it's not eternal, and while it work it becomes impossible to find the leaking point...)
I'll tell you how it unlfolded, but I do hope I'll be able to solve it by my own means because going to the Smart center is not an option!
(the car official value must be around 1000€ now, so I'm not going to put half that sum in a minor repair.)
Thanks again for all your advices and help!