"The biggest crawler/spider/bot(/ or whatever) on this earth is google & I dont think that it is unfair to crawl them(even if it is in their TOC).!"
Actually, that's why they provide an API, an Application Programming Interface, to their products. What you regard as "fair" doesn't come into it. Your educational establishment will likely want you to behave within the law, a reasonable body would actually cover any (probably minimal) costs involved. Since you seem unable to find out how to contact Google I doubt this will have any impact on you.
You don't "need to do it", you simply want to.