All Jews are required to eat kosher. Some choose not to because they believe it's not important anymore. Gentiles are not required to eat kosher but Jews believe that all people, including gentiles should not cause unnecessary suffering to animals.
They can eat a kosher diet, and be slaughtered the kosher way.
Kosher, when dealing with food and diet, simply refers to rules for the preparation and consumption of food. It has no bearing on the quality of diet itself. As such, there is nothing intrinsically good or bad about a kosher diet in terms of health.
The general meaning for kosher is "clean/fit or proper" and if you relate this to the cabbage soup diet, yes it is kosher and can help you stay healthy.
Keeping kosher.
It needs to be cooked in a kosher vessel and have kosher ingredients. If purchased, it (or the bakery) should have kosher-certification.
Yes.
Leviticus 11
Keeping kosher.
See the links.
Judaism. See also:http://judaism.answers.com/jewish-laws/laws-of-keeping-kosher
There is nothing non-kosher in the ingredients for peanut butter and there are several brands of peanut butter that are certified kosher.
Kosher is the diet of Jews. Jews keep kosher. If you keep kosher you cannot eat: shellfish, pork, or dairy mixed with meat. The main land of Jews is Israel. So technically, the nationality of kosher is Israel.