How do I configure my browsers not to save passwords for specific websites?
Since you have multiple questions here, I would attempt to answer one of them:

In case of Firefox:

Open the permissions manager

in the address bar type following about:permissions and hit enter

In the new window select the web site to work on and choose the settings.



To further customize a specific web site (fine tune) click on the small Icon in front of that website address. In the new pop up window you can highly customize what that web site can and can not do.