I changed a bit of the history so it fits better. In short: Severus became a Death Eater with 17 while still in school and a spy with 19. The other changes will become clear by itself.
To the questionnaire, I won't really go into the questions, it's going to be about the complete work and the results because of it. And there will be questions answered what Death Eaters do when they aren't murdering muggles for fun


"Headmistress LeCroix, can I have a few minutes of your time, please?"

The portrait stilled. The Potter boy, what could he want?

"I will decide that after you tell me what you want, Mr Potter."

Al nodded.

"Of course, Headmistress.

I think you are aware that I work on a history project concerning Headmaster Snape.

I did a lot of independent research and Headmaster Snape helps me since 2 months. My project has to be finished in 3 months. I wanted to add a few arithmancy calculations based on his answers.

I'm a third year, Headmistress. I can't calculate the necessary steps, there are too many variables. And I don't want to ask my arithmancy teacher."

Madam LeCroix didn't even had to ask why he wouldn't want to ask Vector. She would tell the boy he wasn't old enough and to wait for the moment he could do the calculations without help. The second reason was clear the moment Al Potter spoke about his teacher, he wrinkled his front. Madam Vector was a competent teacher but she lacked the imagination and perspective neutrality to be really good in her chosen field.

Most students didn't realise that at all and the ones that did didn't find that out in their first year of learning the subject.

Suddenly Al Potter was somebody who would really benefit of somebody supporting him in the field. The boy could work hard, he did so for Severus.

She just had to wait for the question she knew would come.

"Would you be willing to calculate the variables for me? It would benefit Headmaster Snape, I thought you would be interested in helping him."

Oh yes, he was a Slytherin. A very thinly veiled comment to show her he knew about the relationship of Snape and herself. Their little white lie went better then they ever suspected.

For that comment she decided he had to stew a bit in his own juice. She was a portrait, she had all the time of the world after all.

While the boy waited she estimated him visibly. And there she found it, the reaction she wanted to see: uncertainty.

"I'll help you with the calculations under the condition that you learn the calculations and steps to the best of your capabilities. And these capabilities will be decided by me."

Potter thought about it.

A very good idea, Snape was not the only hard taskmaster in the history of Hogwarts teachers. The boy knew that.

"Headmistress LeCroix, when do you have time for a new pupil?"