No. Hanukkah comes out according to the Hebrew calendar, not the Western (Gregorian) one. Hanukkah was founded over 150 years before the onset of Christianity.
Israel is a country so doesn't eat anything. The Israeli population are Jewish and do not celebrate Christmas so they will eat the same food as any other day.
No. There is no "Jewish Christmas". The Jewish Savior is not yet born. Hanukkah is a holiday that occurs around the same time as Christmas but shares no similarities in terms of meaning or purpose.
The same as Jews everywhere.
Only the Jews celebrate Hanukkah, whether they live in Rome or elsewhere. The main observances of Hanukkah, such as its prayers and the lighting of the candles, are the same everywhere.
There is no "Jewish Christmas". The Jewish Savior is not yet born. If perhaps you are asking about Hanukkah, this is a holiday that occurs around the same time as Christmas but shares no similarities in terms of meaning or purpose.
Mexicans who believe in Christmas or who celebrate it, do indeed have a Christmas tree. I know someone who lives in Mexico. It's the same thing, if they are Jewish, they celebrate Hanukkah, if they are Christian they celebrate Christmas.
The same as everywhere else.
Jews in Latin America celebrate Hanukkah in much the same way as Jews around the world. They tell each other 'Feliz Hanukkah', light a menorah, and distribute gifts the same as anywhere else.
Jews don't celebrate anything instead of Christmas. This is because Jesus plays no role whatsoever in Judaism, therefore there is no Jewish holiday to celebrate him. Some people mistakenly believe that Channukah is the "Jewish Christmas", however, this couldn't be further from the truth. Channukah celebrates the rejection of forced assimilation, celebrating Christmas would directly violate the meaning of Channukah.
The same as Jews everywhere.
Kids celebrate Hanukkah almost the same in all countries, but in the US, gift-giving is more common than it is outside the US.
The same as Jews in every other country.