"Kashrut" refers to the Jewish dietary laws. There are many kosher laws. Here are a few highlights:
Most prepared foods must carry certification that their production is supervised, so as to ensure that they comply with these rules. Kashrut certification is generally indicated by an identifiable symbol, in addition to the word dairy or pareve, which means the food is neither dairy nor meat, but rather neutral. (If a package has just the letter 'K' on it, this is not a valid kashrut symbol as the letter K cannot be trademarked.)
Although dairy and meat cannot be served together, fish may be eaten with dairy. This gives rise to the popular and kosher bagel, lox, and cream cheese combination. All fruits and vegetables are kosher.
Meat and dairy dishes and utensils can't be washed together. Kosher kitchens must maintain two sets of utensils, pots, pans, and dishes.
Contrary to popular misconception, rabbis or other religious officials do not "bless" food to make it kosher. There are blessings that observant Jews recite over food before and after eating, but these blessings have nothing to do with making the food kosher. Food can be kosher without a rabbi ever becoming involved with it: the vegetables from your garden are undoubtedly kosher (as long as they don't have any bugs, which are not kosher.)
Foods that Jewish people cannot eat are known as 'non-kosher'.
They eat the same foods as everyone else.
It is never specifically required.
The same foods everyone else ate.
Meat and dairy
Kosher foods.
That depends on what country they're from and where they live. Religiously observant Jews will only eat kosher food.
Orthodox Jews don't, but Jews who belong to other branches of Judaism may or may not eat non-kosher foods, it's a personal decision.
They eat kosher versions of Russian foods.
When God told them to in Leviticus 11.
Orthodox Jewish teenagers eat the same things all Orthodox Jews eat; kosher foods of all different kinds.
Because the Torah has a section detailing what foods are and are not suitable for eating. Jews follow these rules as part of our path to living a righteous life.