I was requested to write a recommendation letter myself so my reference would send it overseas. The problem is that when addressing myself, I used my first name instead of 'Mr + my last name'.
So I would like to know if that is inappropriate, impolite, incorrect or if it would actually say or state that the reference is really close to me.
It depends on the culture, I guess, and also what your relationship with the person was. If he or she called you by your first name, then I would use your first name.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.