I wouldn't say anything unless asked and don't lie. Apply, apply apply..heck, there's lawyers and judges who are ex-cons. Cops with DUI's. Politicians with...you get the point. Don't call yourself out...that's the umpires job. Your job is keep trying to score. If you've been convicted then you have paid a price, quit trying to make it a life sentence. The scars will remain unless you can get them expunged b/c of the age you were, etc. When you can financially afford it I would look at getting an expungement lawyer and see what they can do.
Also, I don't think it's the MSN that's the issue it's whether they are apprehensive about your drug use, state board approval or hospital policies, etc. If they let you take a spot with a conviction but knowing you will not get a job then it takes someone else out of the running. My guess is your hiccups are NOT disqualifiers, you just need some help to wade through it. I would meet with the admissions boards "in person" even if it's an online program. They need to have their concerns assuaged. If you don't want to do NP then get an MSN in something else.
Don't stop...just don't stop. I can't stand it when I hear people who feel like giving up b/c of something you have already gotten past in their life. You're not supposed to be perfect, that's how you learn.