Is there a difference between Nolle prosequi and charges dropped?

No difference, just some fancy Latin!

I will try to answer all of your questions, but you would be better off asking the attorney that represented you. The nolle prosse does not affect your ability to sue, but whether or not a civil suit would be successful is a different story. Your case was dismissed, and whether it was before or after you were indicted does not matter that much unless you were arrested before July 1, 2013. Since your case has been dismissed, you can't go to trial. Expungement, now called record restriction, may be possible. That will obviously impact what a background check might reveal. It is impossible to answer without knowing all of the facts and circumstances. Not sure what to tell you about your top-secret clearance.

nolle pros means the prosecutor didn't think there was enough evidence to go forward. Dead docket would be if the court dismissed the case for another reason. Dismissed with another reason would be something else the court could do. You should speak with an attorney to see how your situation affects your various examples.

You are still free to sue. Keep in mind it is very difficult to sue the government. No, you don't need to go to trial. Even if you wanted to you couldn't. If you were arrested after July 1, 2013 the expungement will be automatic. Just follow up to make sure it gets done.