There are a number of popular foods that are seen consistently around the world. However, it would not be found in every single place in the world, but it would be in most places. Probably the most famous food is pizza. No matter where they come from, people have at least heard of pizza and eat it on a regular basis.
People can make it on their own. Pizza is sold in almost every single country because it is easy and cheap to make. Pizza began in Italy and the best pizza is known to be created in Italy today. In the United States, the best pizza is probably made in Chicago because everyone knows that they have to eat pizza in Chicago.
This is impossible to say. Each country has its specific foods: chips, feature in many countries, fish and chips in UK; popcorn in the US. sushi in Japan. chow mein in China, burritos in Mexico, serrano ham in Spain, rice and peas in Jamaica, all the curries in India. Nasi Goreng in Indonesia. I could go on, but you can already see that there is no one 'famous food'.
What might make one particular food the most famous internationally would be if it was reported to have magical properties, such as the nutrients that caused age reversal. Such a food would certainly have fame following it.