1) Simple file open, write, close.
open (FOO, ">/home/me/afile");
print FOO "hello, world\n";
close FOO;
If you need to have several print lines to the file, you could redirect standard output to your file handle:
select FOO;
This saves you putting the FOO in every print statement. When you've closed your file, you should put your output back where it belongs:
select STDOUTl
2) I've set up tons of stuff based on Perl and MySQL. Yes, they're fast. The bottleneck tends to be the Internet. If you want to really hammer Perl on a busy server, you should probably have a look at mod_perl. This gets a Perl interpreter into the Apache HTTPD web server - significantly quicker than just calling a normal Perl CGI. I've never bothered with this myself as my client sites have fairly low traffic - the Internet is still the big bottleneck.
3) <
http://www.perlmonks.org> The O'Reilly stuff is great - I use the Perl CD bookshelf all the time. I'm not sure that putting a copy on a public web site is necessarily legal - they may get a call from O'Reilly's IP lawyers. If you are thinking about purchasing anything, the CD version is heaps cheaper than buying the books in paper form.
4) Perl absolutely rocks