Upvote:2
There is no immigration leaving the USA (apart from random spot checks).
The only people that will look at your passport are the check-in staff and TSA will check your passport details(name) against your ticket before security.
You also do not pass through immigration on internal flights in the USA.
Upvote:2
The US does not have departure immigration formalities. You do not speak to any immigration agent when leaving the US. You check in, go through security and directly to your departure gate, the same as a domestic flight. Your airline will inform immigration that you have departed.
You don't need to replace your visa to depart the US, or even to remain in the US. It is not possible to replace it in the US anyway. And your F1 status remains valid as long as you are still in the US.
You do need to apply for a new F1 visa in your home country if you wish to return to the US.