I looked in your error logs and I see this:
Premature end of script headers: index.php, referer: http://www.carrinhocompras.com/medicos/novomedico.php?acao=chat
However, reading their directions, you have the phpfreechat folder in the wrong place.
Right now you have it in /home/username/phpfreechat-1.5/
That direction means you should put it in /home/username/carrinhocompras.com/phpfreechat-1.5/
Then you'd change chat.php to be looking for ../phpfreechat-1.5/ (or /phpfreechat-1.5/)