Learn Russian: Мама готовит картофель.

Russian does not have a separate present continuous tense. The single verb готовит means both "cooks" and "is cooking" depending on what makes sense in the situation.

Why does the ending of картофель stay the same if it is the direct object?

Direct objects take the accusative case, but because картофель is a masculine noun for a non-living thing, its accusative form is exactly the same as its dictionary form.

Why is картофель singular when the translation says "potatoes"?

In Russian, картофель is a mass noun. Just like we say "rice" or "corn" in English without making them plural, Russians use the singular form of this word to refer to potatoes as a food type.

How is the word готовит formed?

The dictionary form of the verb is готовить (to cook). To match мама (she), we remove the -ить ending and replace it with -ит, giving us готовит.