Whether to use Dr or Prof when addressing oneself in an email?
Use whatever you feel comfortable with.  That said, you should also tailor it to the type of correspondence when necessary.  A formal letter should include a formal address for yourself, and less formal can be more or less whatever you'd like.  In dealing with students, I generally sign school related emails as "Dr. G.," (with just the first letter of my last name) but I've also taught classes where I've gone by my first name exclusively, and let the students decide how to address me, after telling them it is fine with me if they use my first name.  More formal student correspondence (e.g., if I'm cc'ing another instructor, or if the matter involves the administration) gets my full last name, and correspondence to colleagues is almost always my first name.

I also have a signature block, that includes my title, full name, email address and (sometimes) my telephone number.