How to fix colorsync errors ?

ColorSync reports many errors that aren't errors at all. I'd be more concerned that the video on the system board, the display panel itself, or a cable between the two is going bad.

You can't change privileges because of the new rootless safety aspect. Try google it.

As I said, it sounds more likely to be a hardware issue.

I realize such screen issues can be difficult to descibe in a post, but "layer of distorted colours" doesn't tell us much. Can you take a picture of the screen and post it here? Use the camera icon to upload a photo, or drag and drop it into the editing window. If the digital camera you use takes large images, size it down to no more than 1000 pixels wide, first.

Thank you for the image. Yes, it's definitely a hardware issue. Profiles cannot create such breaks in the display no matter how corrupt one may be.

Take it in to an Apple Store if there's one near you. Expect it to be a rather expensive repair. Being just over a year old, they may, or may not give you a pass and repair it for free, but don't count on it.

If you purchased AppleCare for the Mac before its first year beyond the purchase date was up, then it will be covered for two more years and the repair will be free. If you don't have AppleCare, you can't purchase if after the fact. And the Mac is over a year past its purchase date, so you won't be able to get it anyway.

but it disappeared by its own now … I let is shutdown for two days and it was removed.

I would suspect the problem will return. If not, consider yourself fortunate.

but still i can't fix the errors.

Again - ColorSync profiles cannot in any way cause these kinds of screen display issues. A profile is an overall control of color. It can't, and doesn't manage device color in pieces or strips. Again - ColorSync reports all kinds of things as "errors" that aren't errors. There are all kinds of ways to build profiles, and they still work as expected. Some methods are deprecated, but are still functional, not errors. Here are my supposed "errors":

Searching for profiles...

Checking 102 profiles...

/Library/Application Support/Adobe/Color/Profiles/AnimePalette.icc

Header message digest (MD5) is not correct.

/Library/Application Support/Adobe/Color/Profiles/ColorNegative.icc

Header message digest (MD5) is not correct.

/Library/ColorSync/Profiles/EIZO 11-4-15.icc

Header message digest (MD5) is missing.

Tag 'desc': Identical text could share the same data.

Tag 'dscm': Identical text could share the same data.

/Library/ColorSync/Profiles/JohnRobertsEFI_OverDrive.icc

Tag 'DEVS': Tag reserved field is not zero.

Tag 'desc': Description tag has a bad Unicode string.

/Library/ColorSync/Profiles/JohnRobertsEFI.icc

Tag 'DEVS': Tag reserved field is not zero.

/Library/Application Support/Nikon/Profiles/NKLch2.icm

Header connection space is not correct.

Header data space is not correct.

Header profile class is not correct.

Tag 'A2B0': Number of input channels is not correct.

Tag 'A2B0': Number of output channels is not correct.

Tag 'B2A0': Number of input channels is not correct.

Tag 'B2A0': Number of output channels is not correct.

/Library/Application Support/Adobe/Color/Profiles/RedBlueYelllow.icc

Tag 'pseq': Required tag is not present.

/Library/Application Support/Adobe/Color/Profiles/Smokey.icc

Tag 'pseq': Required tag is not present.

/Library/Application Support/Adobe/Color/Profiles/TealMagentaGold.icc

Tag 'pseq': Required tag is not present.

/Library/ColorSync/Profiles/TIFF RGB

Tag 'desc': Tag size is not correct.

Tag 'desc': Description tag has a bad Macintosh string.

/Library/Application Support/Adobe/Color/Profiles/TotalInkPreview.icc

Tag 'pseq': Required tag is not present.

Verify done - found 11 bad profiles.

Note the third item, my current monitor profile of EIZO 11-4-15.icc (besides others) has the same "error". There's nothing wrong with it. A couple others are those I created with X-Rite's i1 Profiler software. I'm quite sure EIZO and X-Rite know what they're doing.

You also have to consider which profiles you're actually using. If none of the ones you have listed are being used, then it doesn't matter if they're the most corrupt .icc profile anyone has ever seen. "Not in use" = "can't do anything to the system". It's just a file taking up space on the drive.