You are a "SEO Qualification" already so you should know the answer. If you really wanted to use then you may adapt a little like "gooogle" or "goggle" or "googel". Otherwise your website would be marked as copyright infringement.
I think it is allowed.. I do remember reading a thread using a the same wikipedia as the domain name.. though I don't think it is wise for you to do that.. why not build a trademark instead of copying others.. that is more safer and at the same time lesser hassle.
yes, you can use it. As long as you dont become their competitor or make big money, then they wouldnt bother about it
It is a trademark and you can not use it anywhere in the world. If you do, you can have problem with Google if they are interested in what the site is all about. All the best.
Some sites have used it for years such as this site http://www.justfuckinggoogleit.com/ they don't seem to have any problems. Plus there are hundreds of other sites using it in there domain name.
why you say its infringement? Many peopel using "google" in their domains Example : clientsbygoogle.com
This is what Google say- Google-based Domain Names We cannot approve the use of Internet domain names that use the word "Google" or some variation of "Google". For example, we would not approve a site called googleXYZ.com or gogggles.com. http://www.google.com/permissions/#