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"Дорогая" means simply "dear." It is very commonly used in letters etc., including official ones, where it competes with other forms of address.
"Милая", on the other hand, is a bit more personal,...

Yes, Dative is often used in season or birthday greetings, although you could also say something like

"Счастливого Рождества, о прекрасный цветок с прекрасной душой."
But that would sound even...

"Lenka" (which is a very informal form of "Yelena") clashes with the rest of your message. Especially with
"dearest." But if you want it that way, here you go: :crazy:

Дражайшая Ленка!...