An early relieving request asks to be released before your full notice period ends, usually because a new employer has set a joining date. Offer something concrete — notice pay in lieu, a completed handover, or availability for questions after you leave — because early release is a favour, not a right.
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.