A relieving letter request asks your employer to confirm in writing that you completed your notice period and have been formally released from your duties. New employers in India, Pakistan and the Gulf routinely make this document a condition of joining, so send the request in your final week rather than after you leave, and confirm your full and final settlement status in the same message.
In your last week, not after you leave. Once your corporate email is deactivated your request has to go through a personal address, which usually adds delay.
Ask for whatever they will issue in writing — an acceptance-of-resignation email, an experience letter, or a full and final settlement statement. Most new employers accept a combination when a formal relieving letter is unavailable.
Only with your employer's agreement. Many contracts allow you to pay the balance of the notice period in lieu — offering that up front is usually what unlocks an early release.