tl;dr: Whatever you think is a coaster, you can count.
There has always been grey areas in what counts as a coaster, and if you should count it. Some people go off of what rcdb or Coaster-Count has, but of course there are some exceptions in those. Many tend to go the hard definition of "If it's on a track, has wheels, and coasts, it's a coaster". But then that leaves some things like Bobsleds and Powered Coasters to question. Others are really zany and don't even consider kiddie and family coasters. But to most, it's whatever you think is a coaster. Log flumes and dark rides tend to not be counted, since they don't really "coast" at any point on a designated track. But of course, there are water rides and dark rides alike with coaster elements in them. Again, if you think it's a coaster, count it.
As for Steeplechase/Nash: Steeplechase is 3 distinct, separate tracks that happen to be right next to each other. Nash is what's called a Mobius coaster, where it's really one long track that looks like two. You leave one side of the station and arrive in the other. If you want to ride the whole ride, most people do both sides in order to count it.