There's a difference between a complete, grammatically-correct sentence and a greeting.
If I was writing a complete sentence, I would write "I wish you a merry Christmas and a happy New Year." But if I was just greeting someone, I'd say, "Merry Christmas!", not "A Merry Christmas".
It's like when you write a title or a headline, you often leave out words, especially articles and versions of the verb "to be". A newspaper headline will say something like "Stock Market Up", not "The Stock Market is Up".
I suspect people write "Merry Christmas and a Happy New Year", i.e. no article on the first but including an article on the second, because they're starting out writing a headline type of construction but when they get to the middle it's getting kind of long and they put in the article as if it was a complete sentence through force of habit. I think it's inconsistent and I wouldn't do it. I'd generally write "Merry Christmas and Happy New Year!", or maybe possibly "A Merry Christmas and a Happy New Year."
Of course, in these politically-correct times, the correct greeting is "Happy Unspecified Holiday to you, unless the very idea of holidays offends you, in which case please pretend I said nothing and walked past you in silence".
Q1: Is it jealousy of sth or jealousy at sth or jealousy about sth when referring to the reason why someone is jealous?
I would think you would use the same prepositions for jealousy as for jealous.
Paul was jealous of Bill. Paul expressed jealousy of Bill.
Paul was jealous for/over his wife. Paul expressed jealousy for/over his wife.
Paul was jealous for/over Bill's car. Paul expressed jealous for/over Bill's car.
Somebody correct me if I'm wrong, but I believe you can use either for or over with jealous in either of the latter two senses it holds above.
I have never heard that you could be jealous at something or about something, but if the usages are valid, I would expect that you could use them in the same with jealousy.
Q2: Is it common to say jealousy of sb when referring to the person of whom I'm jealous?
Jealousy of/for/over/at/about something is awkward and in my experience little-used. It is more common to say, "I am jealous of him," as in the example first sentences above.
Best Answer
The word usage is wholly dependent upon what you are trying to say with the sentence. Note that the differences, while real, are also minor. Most readers would guess the reason for the gathering.
This implies that the family got together around Christmas time, but does not suggest that Christmas was the reason for the gathering. This can be seen in the following example:
If you are trying to say the family gathered to celebrate the holidays, then you might say
Or