Learn Russian: В супе мало мяса и много риса. - There is little meat and a lot of rice in the soup.

Because of the quantity words мало (little) and много (a lot). In Russian, when you state an amount using these words, the noun that follows must be in the Genitive case. For neuter nouns like мясо and masculine nouns like рис, the Genitive singular ending is -а.

Since много means 'a lot', shouldn't 'a lot of rice' use the plural form of rice?

Not for uncountable things! Just like in English, we don't say 'a lot of rices'. For mass nouns (things you measure rather than count), Russian uses the Genitive singular after quantity words like много and мало.

Why is it в супе instead of just в суп?

The ending -е shows that суп (soup) is in the Prepositional case. This case is used after the preposition в (in) when you are talking about the location of something. Since the meat and rice are located inside the soup, we must use the location case and say в супе.

Where is the Russian word for 'There is' in this sentence?

Russian doesn't usually use a direct equivalent for 'there is' or 'there are' in present-tense descriptions like this. You just state the location (В супе) and what is there (мало мяса и много риса). The 'is' is simply understood from the context.