Is it fine to use the more recent remastered release that is on steam? Also is there any sort of character restriction in NG? I saw in the NG run that Blade was chosen before he would have been unlocked in murderworld. Does this mean that I could use a character such as Nick Fury as long as I choose NG with no save file previously?

That's what we've been doing. All characters are fair game for NG as long as they are on default stats.