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?