I'm not really familiar with how kazaa works but there should be no problems with downloading files through a router or firewall the protection the offer is mainly from in-bound attacks. You just have to setup permission for the application to connect through ZA. And I'm not sure how you'd do that with a router but with zone alram it should ask you for permission everytime it conects unless you set it to automatically give permission.
I know kazaa has specific ports it uses through your router and you have to set permission through those I think?? Have you searched the site for more help I know we've had a few threads in the past about this.
oh and as for your ads welcome to kazaa home of the worlds greatest spyware

better run adaware 6 and spybot s/d and I'd update my virus programs if I was you