For the envelope write the full name i.e. Russell T. Davies. For the letter, it depends on how formal you want to be.

Dear Mr. Davies,
Dear Russell T. Davies,
Dear Russell,

I got Kat Von D's auto just like that. idk if that's actually her full name or not, I was writing for my fiancee. :P

Thank you :)

Yes, I'd say to include their initial. I did this for Kevin G. Schmidt and got a success. {up}

RYAN J. 8)

This may sound slightly pedantic, sorry :?
If a person I'm writing to is usually credited with and referred to with an initial in their name (E.g. Russell T Davis, John C McGinley etc) when addressing the letter should I write out their name including their initial? I usually address the person with their full name, and I'm not sure if you're even meant to do this, so it could even be that I should stick to just the first name and not worry about the intial at all- I'm unsure!
Thanks :)