How does the 68k software install work? Do I decompress the archive and double click Install?
Different from application to application I would say. Chances are some other guy has tried it before you, so begin with searching morpzhone, this site, etc for tips and solutions to problems (if there are any) to the application you want to install. Sure, you could just try using the applications' supplied installer first, but as a general recommendation (and not MorphOS specific one) you should consider doing it manually instead, perhaps with some guidance from the installer script and a system monitoring tool. And sometimes you will need to tweak/alter some things for the program to work properly on a MorphOS system anyway, and no old amiga installer will know anything avout this. So search for info and ask questions at morphzone if you run into trouble.

Do I need 3.1 KS ROM or Workbench disks like AROS?
MorphOS is *not an emulator*, it's a complete Amiga OS that provides its own Amiga API's and Amiga environment fully native. So native "ROM's", "Workbench" (called Ambient in MorphOS), etc, etc is there already.

Even the 68k Amiga binaries are recompiled into optimized fully native PPC binaries before they run.

Ofcourse you can also choose to run the UAE emulator on top of MorphOS, and then you will need those files you mentioned. But running those apps mentioned in this thread inside an UAE emulation box on top of MorphOS would work, but would give terrible performance, relative to running the apps natively on MorphOS...