I'd include the diagnosis, partly to help the school with what to look for, but also to provide a basis for an IEP, as one prerequisite is at least one of certain specified conditions. You should also include the areas where you believe your son needs special help but phrase your letter in a way that those are not all possible areas.
The school first will have to evaluate him, then schedule an IEP meeting to determine eligibility, then proceed to developing the IEP itself. Before they can do any of that, they will need your written permission for their evaluation, so I'd suggest clearly including that in your letter. And, address the letter to the principal and/or director of special education. Some advise sending it certified mail, but I follow the advice to hand deliver the letter(s), making notes of when and to whom it was delivered -- not obvious that you may be building a paper trail that could be important later.
Finally, timelines vary by state, with most allowing at least 60 days to evaluate and meet. That time line starts when they have the request and the permission to evaluate (as well as availibility of your son for the evaluation).