If your relieving letter has not arrived, follow up in writing with the date of your original request attached. Stay factual and unemotional, restate that your exit formalities are complete, and give a specific date by which you need the document.
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.