You are a sweetheart, thank you for posting. Welcome.
You have notification from USPS, they have received your letter, your father is incorrect there. All is fine. Personally I prefer to recommend the email system email@example.com
but you will be fine.
It is not always so that the eccl. matters letter is sent. Administration procedures are changing all the time and I know plenty of people who did not receive this letter.
The procedure is that membership records need to contact your bishop, who needs to ensure with you that you are not being coerced and that you are resigning of your own free will. He then sends a mail, back to membership records also via the Stake, then your membership is disabled.
Sometimes the individual bishops like to sit on the process.
Standard recommendation of time length advised by membership records itself is 6/ 8 weeks for the process to be complete.
In 6 weeks time if you have not heard anything from the bishop, then contact him, if you feel able, to ask where the process is at.
But they will not like to make it hard for people to resign now as it makes them look even more like a cult.
You can check the progress yourself by trying to log in to your LDS account using your LDS membership number and DOB or try to set one up if you do not have one. If you can't, then you are out.
That happened to me, they never sent any final confirmation letter to me but I persisted as it is our legal right to have one and eventually the bishop wrote me a confirmation.
So you can see that people in the Ward and Stake will know and people talk. However, I can see that you are very strong and It is my belief and experience that the bishop etc will not unnecessarily tell people because you have good strong reasons for resigning and they don't like that. They like to pretend to others in the Ward/ Branch that folk have just gone inactive.
I am very pleased to have met you. You go girl and change the world for all of us. Thank you for the comfort that you have brought to the Board today.