I am about to migrate WordPress Installation from One Domain to another which are under the same host and have common cpanel. Besides the first step of backing up and moving the WP filesystem, can we just use the same database without exporting/importing it via PHPmyAdmin ?
If your server is not changed, you don't need to do something with your database. Just leave it as it is.
Additionally I would like to recommend you to read Moving WordPress article from the codex. You will find all answers on your questions about migration.
Followed http://codex.wordpress.org/Moving_WordPress and that seems to be the best thing to do.