A title change request with no salary change is the easiest ask to approve and the one most people never make. Frame it around external accuracy — clients, candidates and your CV should reflect the work you actually do.
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.