Stationery pad is the classic mac os term for a template, so each time you run it it's making a copy for your further use.
I'm not aware, when something is compatible with both, of a way to force something to run in Classic Mode, and for almost any software that can (e.g. Photoshop 7, Final Cut 3) you wouldn't want it to run in Classic Mode, it'll be more stable and possibly even faster under OS X.
For data files, tough to say, I'm not aware of a way to set the default associated program so you might just... drag them onto the app you want to use's icon?
These are applications not data files. It's like sometimes Mac OS X is not understanding where the resource forks are. My Powermac G4 died so I have moved Classic to my Mac Mini. I drag the archives off my flash drive to the HD as I have always done on my G4. I extract them on the Mac's hard disk. As I said in the opening post, the programs then open in a text editor or Automater. This only happens with some applications. The Universal Hint System(UHS) reader is one such program. I guess 'Stationary Pad' works cause it reassembles the Resource Fork?
Before I relized the UHS reader was an OS X program(cobinated?) I wanted to try and say "open this with Classic".