After a lot of tests...
I've got the best results (clean pics, trasparency ok, white and black ok), with this settings (Save for Web, Photoshop):
=> On the left
PNG-8
"Custom"
No Dither
[X] Trasparency
No Trasparency dither
=> On the right
[X] Interlaced
Colors: 220 (or 256)
Dither: disabled (gray)
Matte: a blue...
Amount: disabled (gray)
Web Snap: 100%
Thank MIDAS!