I have .png image which represents relief shadows. I need to save it in Photoshop 1-bit .png. Can someone help me, please?
Do you mean 1-bit as in black & white or single color with an alpha channel?
Just about any imaging app can do both - an image converted to black & white in M$ Paint, is essentially a 1-bit image. In PhotoShop, you can create a regular 8-bit image, File->Save for web, set it to PNG-8, transparency ticked, then set the number of "colors" to 2.
It would be the same as the black & white image, but a color (yes, black counts) & alpha channel (transparency).