The only ones I'm aware of recently that recommended a hardening fixer were Efke films, and they're gone. The Foma films are definitely softer and easier to scratch then Kodak/Ilford/Fuji but you can probably get by without it if you are careful with the wet film - very careful. Of those, I don't know who makes the "Agfa" branded film now and I don't know about the Adox. The Pan F and Delta won't need hardener.
It can be used with any film but you need to be careful with films that are not prehardened by keeping the temperature of the developer, stop bath, fixer and wash water close to previous bath.
Think CMS is prehardened the others you quote are.
The Adox CHS 100 type I was not prehardened the type II probably is.
There are web data sheets for most films google and down load.
Sometimes the card box the film came in has more details.
If you do use a hardener then you need to increase wash time.
Kodak and Ilford provide web 'how tos' for home processing, google and download.
I've used all the softer emulsion films like the EFKE range and Pomapan in non hardening developers for a few years now with no issues in hon hardening fixers,
Sodium Sulfate is indeed used to prevent scratching of soft films. Sodium Sulfite is also added as a preservative.
Most modern films from Kodak, Fuji and Ilford are hard enough that a hardening fixer is not needed, but others may need a hardening fixer and this must be determined on a case by case basis.
I do presoak with the Jobo. But still if you are very careful the Foma should be ok. I wouldn't use a squeegee on it, but then again I'd never use a squeegee on any film.
Sodium Sulfate is indeed used to prevent scratching of soft films. Sodium Sulfite is also added as a preservative.
Most modern films from Kodak, Fuji and Ilford are hard enough that a hardening fixer is not needed, but others may need a hardening fixer and this must be determined on a case by case basis.
Hardening fixers do not hurt today's super hard films. As said above, wash well as the swell will be low and wash rates will need to be longer. The standard retained hypo and retained Silver tests will help determine the time.