C++ (gcc), 181 bytes

#include <string>
auto m(auto s){s[0]=s[0]&~32;for(int i=1;s[i];)s[i++]=s[i]|32;int n=s.length()-1,b=s[n]=='y';return s+(b?"":"y")+" Mc"+(b?s.substr(0,s[n-1]=='e'?n-1:n):s)+"face";}

Note that clang will not compile this due to the use of auto in a function prototype/return type.

Credit goes to Kevin Cruijssen for the &~32 trick.

Try it online here.

Ungolfed version:

#include <string>
auto m(auto s) { // abuse of auto, input and output are std::string
    s[0] = s[0] & ~32; // convert the first character to upper case
    for(int i=1;s[i];) // iterate over the rest of the string
        s[i++] = s[i] | 32; // converting it to lower case
    int n=s.length()-1, // the position of the last character
    b=s[n]=='y'; // whether or not the last character is a 'y'
    return s+(b?"":"y") // append 'y' if not already present
    +" Mc"
    +(b?s.substr(0,s[n-1]=='e'?n-1:n):s) // remove one, two, or zero chars from the end depending on b and whether the second to last character is 'e'
    +"face";
}