Firefox 3.0.5 is a really old version of the browser and this can be the main reason why you have problems with it. In order to fix the issues, I recommend you update the browser to the latest version. In Firefox 35.0.1 you can use the address bar like a search engine. Just type anything you want and press Enter. Also, it comes with a search box that can be customized as you want:
If Google is not the default search engine after you update the browser, go to Settings > Options, open the Search tab and select Google from the drop-down list:
