How can I get my own customised Google search page like Firefox? Example: http://www.google.co.uk/firefox
Also, can I earn from Adsense like that?
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You can build your own Custom Search Engines using Google then monetize it using AdSense. I think the idea is to find useful links on a topic and build a niche engine. I don't know much more than that myself as I haven't used it, but you could start from the documentation page at http://www.google.com/cse/.
Write your own web browser and then make Google the default search engine. Google may pay you $57 million so you probably won't need to use Adsense.