This letter is from Ministry of Health (Training section), they have specific form and issue it to you in the same day. The problems are, you have to have work permission from your work or to be a free doctor without governmental job with a certificate from El-Nekaba indicating that. Since you are still in 4 th month emteaze you can't do that, you should be a member in elNekaba so they can issue you the certificate, directed to ministry of health. This letter should include one speciality only and you should get it if you matched in US program first and at that time you know what speciality you are going. The ECFMG needs your US residency contract along with this letter, fees and other few things to issue you the visa.
The final diploma (cartoon one) is very important piece of document by which your ECFMG certificate could be certified and should be mailed directly to the ECFMG. The latter will write to the university and medical school directly to have transcript and diploma mailed directly to ECFMG, you don't have role in that at all. If already the diploma and trascript issued, which is not yet your case, it takes from 2 to 6 months to be mailed to the ECFMG who confirm it in anoter weeks or so.
I think you have to take the USMLE exams first, this does not need any thing except to fill out the forms, pay the fees and sit for the exam in Cairo or any where (step1 and 2 CK) and step 2 CS only in US by any order you want and leave the certificates and all these issues for the time being.