Does pushing a register empty that register?

Question

I have read many books and instructions on this, but one thing that is never specified is what happens to a register after you push it on the stack. For example if you write in

Answer 1

The register keeps its value after push instruction.

push effects two places: the stack memory that get new value, and the value of esp which now points to the new top. You can deduce that from the description of push operation:

if(StackAddressSize == 32) {
    if(OperandSize == 32) {
        ESP = ESP - 4;
        SS:ESP = Source //push doubleword
    }
    else { //OperandSize == 16
        ESP = ESP - 2;
        SS:ESP = Source; //push word
    }
}
else { //StackAddressSize == 16
    if(OperandSize == 16) {
        SP = SP - 2;
        SS:ESP = Source //push word
    }
    else { //OperandSize == 32
        SP = SP - 4;
        SS:ESP = Source; //push doubleword
    }
}

source: https://c9x.me/x86/html/file_module_x86_id_269.html

https://c9x.me/x86/ is a great pocket reference for x86 instructions, use it at will!