Preferable/Advisable, instead of submitting other bank's details/cancelled cheque or waiting for DD or Banker's Cheque to get delivered physically. It takes time and bit inconvenient.
Depends from bank to bank. Some take closure request online as well, most likely, self declaration/consent is enough usually taken via Mobile/ Internet Banking, e-mail, call & links etc. and some don't & ask only to visit branch physically, where you will be required to submit closure request form and others if any.