"Prompt" is a noun in this case.
The definition in the Oxford English Dictionary is this (I've added asterisks to indicate the important part): "Something said or done to aid the memory; a reminder; spec. a word or phrase spoken to remind an actor, reciter, etc., of a forgotten word or line. Later also more generally: **anything which when seen, heard, etc., acts as a stimulus or guide to some action; a cue.**"
A "prompt" on an exam is the "cue" that tells you what to do. For example, you may see an exam with a prompt such as "Write a two-paragraph essay describing your city," or "Analyze the poem below," or "Underline all of the adjectives below." These are "prompts" rather than questions, because they don't ask you a question. They tell you to do something. In some cases, an "essay prompt" is simply a topic for you to write an essay about. That's probably what the "topic prompt in Part 2" refers to. Part 2 will give you a topic to write about, and then you'll also have to have a more abstract conversation about the same topic.