If the form you are looking at is here, it's a bit ambiguous - at first blush it appears to anticipate that the original charge might be different from the charge that was dismissed, but if that were the case I would expect the form to require the NJSA citation both times. If it were me, I would either fill out #4 with both the name and relevant NJSA citation, or add to #2 something to the effect of "This charge was reduced by the Superior Court to [offense], [NJSA#], then reference that reduced charge in #4.
I don't know anything about the dismissed TRO, so I'm not going to comment on whether or when it might "show up" in a future background search of one form or another.

