TeX has the \read and \write primitives for reading and writing to files plus of course \input for inputting an entire file 'here'. If you look at for example the LaTeX cross-ref mechanism is uses \write but avoids using \read (line-by-line) in favour of making use of \input with appropriately designed secondary files.
As \input is easy enough to understand, lets focus on \read and \write. Both of these work on a file stream, which is given a number but is usually allocated using \new.... For example
\newread\myread
\openin\myread=myinput %
\newwrite\mywrite
\immediate\openout\mywrite=myoutput %
will set up a read called \myread and a write called \mywrite. Notice that I've used \immediate with the \write: due to the asynchronous nature of the TeX page builder, you need to make sure that you ensure that \write operations happen in the 'correct' place. (More on this below.)
With two streams open we can for example write to the output. If we do two writes, one 'now' and one 'delayed'
\def\foo{a}
\immediate\write\mywrite{\foo}
\write\mywrite{\foo}
\def\foo{b}
Hello
\bye
the result is myoutput.tex reading
a
b
That's because \write\mywrite produces a whatsit that is only executed when a page is shipped out. That's useful if for example what you need to write contains a page number, as that is only known during the output stage. Also notice that \write acts like \edef: everything gets expanded unless you prevent it using \noexpand or a toks. Note, however, that this expansion is performed at the moment the \write operation is actually executed, so one must ensure macros have proper definitions when using a delayed \write.
The \read primitive reads one line at a time (unless braces are not matched) and tokenizes in the normal TeX way. You can arrange to loop over a file one line at a time using the \ifeof test on \myread, but as I say it's often easier to simply \input a file containing cross-refs.
If you want to do a system call, 'pure' TeX doesn't really help. However, Web2c has for a long time had a special 'stream' to allow escape to the system: \write18. This is a security risk and so as standard only a restricted set of commands are allowed in such an escape. You can do for example
pdftex --shell-escape myfile
to allow all escape: the risk if you've written all of the code yourself is only in making a mess-up! Doing a \write18 doesn't feed anything back to TeX: you'll need to arrange to read the result in some way, probably using \read on a secondary file.
As noted in a comment, an additional syntax extension available is \input|"<command>". This is again restricted by \write18 but does provide an expandable method to grab input from shell commands.
texdoc texbytopic. About the second question, look forshell-escapeon the site.manmac.tex, the macros that knuth used to set the texbook (and other manuals). both cross-referencing and writing out of index terms are implemented there, and you can see intexbook.texexamples of the input used. (these are rather different from the latex approach, and indeed, from most other definitions i've seen. but obviously, they work effectively. both files are present in the tex live collection.\input), so I thought it isn't explained in it. But actually I was wrong. Next time, before asking a question, I'll consult more deeply my manuals :)