About !define

I used InstallOptions to give users an option while installing,
then define a symbol by their choice. I would use the symbol in
my uninstaller.

If I define the symbol by "!define SYMBOL value" in a hidden section,
will the ${SYMBOL} exist to last in the uninstaller?

Define's are compile time constants. You can't set them at runtime.
You can't define something according to the user runtime request.

To set some value and then use it upon uninstalling use the registry (WriteRegStr and ReadRegStr).