Modify php script

There are two little changes I would like to be made
to a proxy script. You can test the script here
http://beckoningcat.com/proxy/index.php
The code is here http://beckoningcat.com/proxy/index-.txt
The script can not access some sites. For example if you
type Google.com it works OK but if you type
monroecollege.edu you get an error message.
Some sites can\'t be accessed without typing \"www\"
Look at the code where it says \"SET URL\"

The other problem is the log file. I\'d like to keep a
log for as long as I want, but as the script is written now,
log.txt keeps getting bigger, that\'s impractical.

Depending on your interest (and the cost) some other modifications
can be done too. There are other features that the script\'s author
never got around to doing.