I'm looking for the documentation of all the syntax and built-in functions in C, but I can't find any site online which seems like an ultimate official source of standard C knowledge.
Apart from the famous book by Kernighan and Ritchie, isn't there any online C specification? Maybe there is, and I don't know how to find it. Or maybe the problem is that I don't exactly know what I'm looking for.
You can obtain a PDF copy of the C99 standard (ISO/IEC 9899:1999) from ANSI (and other fine standards organizations) for your private use for a modest fee - I believe it was 18 USD when I bought mine. Having that available is invaluable to me. But if you find a copy in public, then it is contraband.
You can find final committee drafts and current working documents of the C (C0x) Standard Committee at the JTC1, SC22, WG14 web site at the Open Standards Organization. (That's Joint Technical Committee 1, Sub-Committee 22, Working Group 14, I believe).
There is also a hardback book 'The C Standard: Incorporating Technical Corrigendum 1' (also including the Rationale) available for a slightly less modest 85 USD or thereabouts.
One of the best books about C is 'C: A Reference Manual' in its fifth edition. However, you asked for 'ultimate official source of standard C knowledge', and the only 'official' such source is the C standard, plus its corrigenda.