In this case you don’t use startS and endS as you have formatted a question with DOES. However in the answer you need to use….. the class starts and ends ….. What does she want? She wantS to invite you …… What does this mean? This meanS ……..

In the sentence "Your class does start" it is the verb "to do" that gets conjugated as the third person singular "does". The verb "to start" does not get conjugated, but remains as an infinitive. Similarly, "The boy does jump" (not "the boy does jumps) "The horse does run" (not "the horse does runs)

“What time does your English class start and end?”is grammatically correct.

Almost. What time does your English class start and end.? No S on the verbs

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