1) You can set all pc to have static ip even though your router masquerading dynamic ip. What you need is to edit /etc/network/interfaces in every pc.:
Remove any dhcp statment and change with static.
Example:

auto lo eth0
iface lo inet loopback


iface eth0 inet static
address 192.168.0.5 ** static ip of your pc.
netmask 255.255.255.0 ** every pc and router must have same netmask
network 192.168.0.0
broadcast 192.168.0.255
gateway 192.168.0.1 ** gateway= your router ip

2) Your QA server should run apache server if you want your client to access it through internet. To run apache server run this command in root konsole: /etc/iinit.d/apache start.
Or run this command: update-rc.d apache defaults ...if you want apache to run automatically on boot. The default knoppix workspace for web is in /var/www.
You can point apache to read or point it to other folder by editing /etc/apache/httpd.conf.
Register a domain name if you want it to be access from outside (net). Or you could register freely available dynamic domain name service out there, ex:dyndns.org.
To test from client without going through net, just point browser to your server ip.