Learn Russian: У нас мало муки и мало мёда.

They change to the genitive case because of the word мало (little/not much). In Russian, words that measure quantity like мало, много (a lot), and сколько (how much) require the noun that follows them to be in the genitive case.

I know that feminine nouns ending in -а usually take an -ы ending in the genitive case. Why is it муки with an -и?

This is because of a very important spelling rule often called the 7-letter rule. It states that you can never write the letter ы after the letters к, г, х, ш, ж, ч, or щ. Since the stem of мука ends in a к, we must use и instead, making it муки.

Does мало mean the same thing as маленький (small)?

No, they are used differently. мало is an adverb that refers to the quantity or amount of something (meaning little, few, or not much). маленький is an adjective used to describe the physical size of an object, like a small house (маленький дом).

Why does the sentence start with У нас to mean "We have"?