Your translation means "You don't do it." "Haga" is in the imperative or command form, and can also be the present subjunctive mood. Check out wordreference.com or spanishdict.com and go to the conjugation section to see the different conjugations. Studyspanish..com has good explanations for the different tenses. Hope that helps.
That's correct. By itself, "I don't do it" would be 'No lo hago'. However, if you have a verb in the beginning of the sentence that triggers subjunctive, you can have 'No lo haga' meaning "I don't do it" but we often don't say it in that way in English.
For example: My son starts fussing when I try to help him do something so I might say "Qué? Quieres que no lo haga?" = What? You don't want me to do it? (lit. You want that I don't do it). In this example, the subjunctive is being triggered by the verb querer, expressing desire. But you see that the literal translation is not how we would natural word it. Hope that helps!