Yes you need to configure your gateway to your router ip. It can be done using network card configuration utility under knoppix icon or manually edit /etc/network/interfaces. Another thing to check is /etc/resolv.conf, this is where your DNS server name reside. Some ISP need you to set their dns so you can surf net.

To run apache, run this command in root konsole : /etc/init.d/apache start.
To start apache on every boot automatically, run in root konsole: update-rc.d apache default
To remove apache from every boot: update-rc.d -f apache remove
Your webpages should be in /var/www by default, only root has access to this directory. You can change this default directory to somewhere else by editing /etc/apache/httpd.conf.

To make live easier while working in kde, you might want to install service menus. I would suggest, Open as root, it makes it easier you to access folder as root. You can get it from http://www.kde-apps.org/

Thats about it.