What mad solder type is used for BGA?

Thermal inertia is playing against you. Also take into account that lead-free solder needs temperatures in excess of 220°C to melt down (compared to 180°C for tin-lead solder), so the thermal gradient will be quite high to begin with.

Because of this, I would recommend preheating the board to 120°C by using one of the following methods:

• A preheating plate, or
• An oven

Then apply hot air to desolder the BGA chip.

BGA have a very good thermal contact with PCB- total cross section of all balls is a quite large figure. So before solder type, all PCB is sinking the heat from your BGA. So you have to preheat all of it to 150C, then power flow will become much lower (delta T is lower) and then you will not need more than 300-350C.

I think you should measure the temperature of your rework station nozzle and soldering iron with a pyrometer. You think your nozzle was at 400°C and your iron at 350°C, but I'm willing to bet they really weren't that hot. Any reasonable solder will melt above 300°C.

On a practical note, if you want to salvage BGA components and don't mind to destroy the PCB in the process, a small gas torch heating the backside of the PCB works wonders: larger chips just fall off by themselves, and a gentle shaking of the PCB removes the smaller SMD components as well. Don't try this inside though (or while wearing nice clothes), as it takes some practice to avoid overheating the PCB. Fumes from burning PCB are toxic and the smell is very long lasting.