The correct answers are I didn't wash the dishes because we have a dishwasher!, You didn't buy any milk yesterday., and The cat didn't get its dinner on time.

To form the negative past simple for most verbs, we use did not (didn't) + the base form of the verb (wash, buy, get).

"Didn't went" and "didn't worked" are incorrect because you cannot use the past tense form of the main verb after "didn't".