The days after a strong review are the highest-leverage moment to ask. Quote the review's own language back, then connect it to the next role's requirements point by point.
Both. Raise it in a one-to-one first, then send the letter as the written record your manager can forward to HR and their own manager.
Measurable achievements, responsibilities you have taken on beyond your job description, and a direct comparison to the target role's requirements. Tenure alone is the weakest possible argument.
After a strong performance review, at the close of a successful project, or during the company's planning cycle when headcount and budget are actually being decided.