OK, it was my first time, I thought it is a pretty straightforward
thing to do, but it looks as if there is a very small friction between
the pads and the disk when I'm not pressing the brake pedal. At high
speed 40+mph I can hear it.

I used white grease between shim and pad. I did like the mechanic,
after removing the two pins, I used a pair of plier to push back the
old pads in order to create space to insert the new one as they are
thicker and wouldn't fit otherwise. I did not remove liquid from the
brake system.

Any help/suggestion would be greatly appreciated.

P.S. I even removed the wheels a second time to have a look and tried
applying some white grease on the pins hoping it would make the
sliding of the pads easier.