I want to know about such a webhosting website which is totally free and provides high bandwidth data transfer with my own domain name?
This is unlikely. What did you have for bandwidth requirements? Any reason you need to stay with free providers? They will usually have these limitations in place, thats why there are paid solutions. If you have something to offer the host like advertising or links they may be more inclined to work with you towards a solution, best way to find out is by contacting them.
IF you want to run your web site fast and efficiently, you'd better choose stable paid hosting services.
Nothing's free now-a-days with your preferred system specifications, I suggest go ahead and purchase a managed hosting.
What is the site? I want to host a site for free on a trial basis - I do not mind paying, but after I have tested the free service. I tried byethost free account, but their wordpress seems broken. They have wordpress 2.85, and it does not allow me to change themes.
send me a pm with: -website address -username -mail address and i'll make a new account for you and you will be able to test everything you want