Yes you can change the copyright
1) For my website, can I change "Copyright ©2012 Mono Ltd." to "Copyright ©2012 MY WEBSITE NAME" ?
Yes, you can add a link with the same text as long as it points to the same url.
2) I know for removal of "Powered By Monox" there is a fee, but if I plan to keep using it as free project, Can I remove "Powered By monox" because it is an pic/ image and it doesn't go with my design and create a link that says "Powered by Monox" and it will be linked to monox website ?
You only have to add back link to MonoX in order to use the product for free, maybe this statement is not very well put.
3) Or I am wrong ? Fee is for copyright message and NOT "Powered by monox" message ? The license says "MonoX Copyright Notice Removal license allows you to remove the MonoX copyright notice and rebrand all sites running on top of MonoX on a single "
No, see my answer on 3)
4) OR we have to keep both messages to use monox as free project ?