Type which installer in a shell and report back. I suspect you have multiple copies of Installer throughout your path. You fixed one by adding the executable bit, but it's not the one being called by default.
The "file not executable" error you got in the shell is the same reason you're getting the "Unable to open your tool 'Installer'" error in Workbench.
In the future, remember to extract everything on the Amiga to preserve the protection bits. And get DOpus 4.16 from Aminet to make your life six zillion times easier.
