I don't know about the rest, but open(), close() and bcopy() are not in the C standard library. They are either POSIX or Linux specific. The C standard library functions for files start with f e.g. fopen(), fclose().

On a tangential topic, I don't know of a good reference for exploring what is included in the standard library.

The classic book The C Programming Language covers most, if not all, of the standard library. The whole thing can be found in an appendix. Admittedly reading an appendix isn't normally the best way to learn about something, but the library is so small and the amount not already covered in the text is even smaller so it wouldn't take long to skim. Of course it doesn't cover Unix-specific functions, like the unistd.h header; for that, I recommend Advanced Programming in the Unix Environment.