Learn Polish: Dodała miód zamiast cukru. - She added honey instead of sugar.

The preposition zamiast (instead of) requires the noun that follows it to be in the Genitive case. So, the basic dictionary form cukier becomes the Genitive cukru.

Why does the Genitive form of cukier end in -u rather than -a?

Masculine inanimate nouns in the Genitive singular can take either an -a or -u ending. Uncountable nouns, substances, and bulk foods like sugar almost always take the -u ending. Also notice the fleeting vowel: the e in cukier drops out when adding the ending, making it cukru.

If miód (honey) is the direct object being added, why didn't its ending change?

It actually is in the Accusative case! Because miód is a masculine inanimate noun, its Accusative form is identical to its Nominative (dictionary) form. It only looks like it hasn't changed.

Could I use the verb dodawała instead of dodała?

Yes, but it would change the context. Dodała is a perfective verb, meaning she completed the action of adding the honey on one specific occasion. Dodawała is imperfective, which you would use to say she was adding it or she regularly added it over a period of time.