A promotion request letter makes the case that you are already doing the next role and should be recognised for it. Lead with outcomes and numbers rather than tenure — the strongest version of this letter reads like evidence, not a request, and gives your manager something they can forward to their own boss.
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.