Most of our cuisine (once it's kosher) isn't bound by Jewish law. For that reason, there's a lot of variation in such a minor matter as what is served at meals.
1) These are necessary at Shabbat and festival meals: bread and wine. Slightly sweet, braided challah-bread is customary; as is sweet red wine.
2) These are long-established customs: fish (typically gefilte fish, and especially at the evening meal); and cholent at the morning meal. Cholent is a slow-cooked stew of barley, meat and beans, with other ingredients to taste, but each family adjusts the basic makeup of the cholent as they wish.
3) These are common: soup at the evening meal; especially chicken soup (that's the famous "Jewish chicken soup" with its reputed healing-properties). Egg salad with chopped onions, and/or chopped liver.
4) Other dishes, including dessert, will vary according to family or community habits and taste.
The Jews eat the Passover Seder meal on the night of Passover (Pesach). It makes little difference whether Passover begins on Shabbat or on a weekday. Note that there are festive meals on every Shabbat, but they are not called "seder" and the foods are different.
A Jewish traditional bean and meat stew that we eat on Shabbat morning.
There is no prohibition against eating kosher meat during Shabbat. The reverse is true; it's expected that meat be eaten during the two main Shabbat meals. On Passover, Jews cannot eat leavened bread (whereas they can at other times of the year). Shabbat does not mirror this. The same kosher rules for the rest of the week apply on Shabbat. Jews cannot eat pork on any day of the week and conversely, Jews can eat tuna or kosher meat on any day of the week.
They pray, eat, pray, and eat some more. And sit around and shmooze a lot.
Yes, if Yom Kippur falls on Shabbat. However, during a regular Shabbat, fasting is a violation of celebrating the day. Instead, the Torah specifies that Jews are supposed to eat 3 delicious meals as part of celebrating Shabbat.
There is no prohibition against eating in a restaurant during Shabbat. Shabbat and kashrut observant Jews would require that the restaurant be kosher. To get around the issue of not being able to handle money during Shabbat, kosher restaurants will pre-sell meals. Additionally, the restaurant would have to be within walking distance.
They prepare their children for Shabbat and light the Shabbat candles.
"Shabbat Shalom!"
The Torah specifies that one should eat at least two types of meat for Shabbat dinner. There are no other requirements specified.
They're called Shabbat candles (Neirot Shabbat in Hebrew).
Shabbat Shabbatot
After Shabbat, there is the Havdalah service.