In any academic writing, it is appropriate to use the word you, as in: When you read the research, you know that the death penalty does not deter crime.

I see the teachers are still injecting their political agenda into homework assignments.

I don't believe you could be penalized for it, but technically using the word 'you' is not proper English. You should be using the word 'one'.

No, it is not appropriate. And avoid using "one." Instead, recast the sentence -- The research shows that the death penalty does not deter crime.

Also, do not speak in the first person.