As far as the internet is concerned, the computer name is irrelevant. In order to access your website with *amit-knl.com address (note that you appear to have misspelled http as hitp), you need to register the address with a DNS registring service (for which you will have to pay a monthly or annual fee). Then, you will have to make sure you have a static IP from your internet service provider (such as BSNL or Airtel). [Well, you can do it without static IP but the workaround is a bit elaborate].
Now, to the main part of your questions... The www is prob. not required, but that is because it is taken as default. For example,
www.yahoo.com and yahoo.com will both direct you to the same site but mail.yahoo.com will direct you to a different site. This is because the address (DNS name) is read from back to front... The com is first figured and then yahoo is figured. If www is not provided, it will be assumed... But if something else is provided (such as mail in the above example), a different page from the same server is returned...
Regarding the second query, I think there shouldnt be a problem unless the proxy mechanism has been instructed to either block your site specifically or in general - but I am not very sure about this...
Arun