What are the fuller expressions of the Russian equivalents to some common festive greetings (e.g., Happy Birthday, Happy Easter, Happy New Year's)?

Question

Even Duolingo will tell you that

Greetings and other similar expressions are often shortened versions of longer phrases, where words still retain their forms.

When you see an oblique form (i.e., a declined form) of a phrase, it is an indicator that it is often part of a longer phrase and one in which the declination makes grammatical sense.

So, maybe if I knew the fuller expressions of these Russian phrases, they would make more sense to me. Below you will find what confuses me about these phrases:

This latest exploration into Russian all began when I tried to figure out how to literally translate the phrase:

С днём рождения!
Happy Birthday!

word-for-word/literally. I then wondered why the "c" was even used at all. I then realized I really didn't know for sure what the literal meaning of this phrase was. I then noticed that

Happy Easter! ∼ Счастливой Пасхи!

I got to wondering, If this is a shortening of the longer phrase "I wish you a Happy Easter!"

Я желаю вам счастливой Пасхи!

then shouldn't "happy easter" be in accusative case? And if so, and Пасха is feminine, then why isn't Happy Easter!:

Cчастливую Пасху!

What case is "Счастливой Пасхи!" in? I am assuming both words are in the same case, but if I am mistaken, please let me know that, too.

Furthermore, if a form of the word "счастливый" is used to express "Happy Easter" why isn't it used when wishing one a "Happy Birthday"? Is Easter the only holiday that uses "счастливый" for a greeting such as this?

Happy New Year's appears to mirror the Happy Birthday construct with:

C новым год!

but again, how does this break down literally, and why not use a form of "счастливый" to express it?

Merry Christmas appears to use both forms if Reverso is any indicator

С Рождеством!
Счастливого Рождества!

but again I'm not entirely sure about the literal breakdown or use of case.

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Are there any other holidays Russians typically front with "Merry" or "Happy"?

Answer 1

We commonly use two structures for congratulations and wishes:

• поздравлять с чем-то (Instrumental)

• желать чего-то (Genitive).

The case used depends on the verb, and should be learned by heart.

So (поздравляю) с днем рождения, с Новым годом, с Рождеством, с Пасхой.

(Желаю) счастливого Рождества, счастливой Пасхи (neither is quite typical for us, but both are possible), or хорошо провести праздники.

Languages differ as do traditions. Why should they be alike?

Answer 2

"С днём рождения!" - ПОЗДРАВЛЯЮ с днем рождения !

или, если совсем полно : я поздравляю тебя с днем рождения ! :).

"C Новым год!" (тут у вас ошибка с падежом) - с Новым Годом! - то же самое : поздравляю с Новым Годом ! "but again, how does this break down literally, and why not use a form of "счастливый" to express it?" Есть и такое : "Счастливого Нового Года !" - и это пожелание, а не поздравление. :)"Желаю вам счастливого Нового Года!"

Форма "Поздравляю с ...", " с ..." применима к любому именно празднику. Но не к памятным грустным датам.