You shouldn't. Hanukkah and Christmas are no necessarily on the same day, so it would be inappropriate to wish someone a happy Hanukkah on December 25, if that day isn't during of Hanukkah.
A better idea would be to look on a calendar to see when Hanukkah falls, then then wish your Jewish friends a Happy Hanukkah on Hanukkah.
The traditional greeting is 'chag sameach' which means happy holiday. To be more specific for the holiday of Channukah you can say 'chag Channukah sameach'.
You say, "Happy New Year" or "Shana Tova".
The question answers itself.
You say "Happy Hanukkah".
Yes.
Yes.
To wish someone a happy birthday in Chuuk, you will either write her a message or buy her gift.
Yes, but only if you are talking to a group of people where some are Jewish and some are Christian.
Happy Saint Nicholas Day!
congratulations......happy anniversary..........
Give them what they love.
You can say, 'Thank you! And Happy New Year to you too!'when receiving a 'Happy New Year' wish from someone.
You can say "Happy birthday Sister" or "Happy birthday (insert her name here)"
You cannot wish someone a happy birthday unless you send them a PM. But, you can go to the directories and there is a button at the bottom that you can click that says, "See todays birthdays." You can congratulate those people.
You can wish people happy birthday in many ways. Nowadays people wish each other happy birthday on facebook, send greeting cards to one another, and also exchange gifts.
It is called a belated birthday wish. Definition: Belated: late, after, delayed, coming after.