can i have the backup of the contacts which are in my contact list and saved in my phone to some other microsoft account or in any way possible such as uploading it in (.csv) format directly to other microsoft account.
Whatever Microsoft account you are signed on using in your phone now, the contacts are being synced with that. Just log into that account -->export -->log into the new a/c --> import.
Go to outlook.com and click on the dropdown on the top left hand side and select people, that's where all your contacts are.