There are a lot of details here, and someone else will have to give the fine specifics, but there are a couple of different types of fixers. There is plain hypo, which is one compound, there is rapid fixer, which is an ammonia-based compound and which does not require HCA, and then there is, for lack of a better term, fixer, which does require HCA.
Rapid fixers convert unused silver to a compound that rapidly washed out while 'regular' fixer converts it to a compound that does not. The HCA step does not negate the fixer, but converts the compound created by regular fixer into a compound that does wash out easily, hence the shorter wash times when HCA or 'rapid' fixer is used.
As I understand it, hardener helps to protect the emulsion (print and film) when it is wet and is not required with many modern film emulsions and only with paper emulsions when they will be wet for a long time or at high temperatures. Hardener does have an effect on the end print result in that toning is more difficult to accomplish well when a hardener was used on the print.
As far as stop baths go, there are different types, but they all do the same thing - change the pH so that development stops. I use water for a stop bath because my film development times are longer and I prefer to use a rapid fixer, which does not work well with an acid stop bath. I use it for prints because of the fixer I use.
- Randy