How to get reference to module by string name and call its method by string name?

To get the module, you can use globals. To get the function, use getattr:

getattr(globals()[module_name], function_name)

Importing a module just binds the module object to a name in whatever namespace you import it in. In the usual case where you import at the top level of the module, this means it creates a global variable.

Get it from sys.modules with a FQN module name like "apackage.somemodule":

import sys

getattr(sys.modules[module_name], function_name)

Use this if the module name and/or function may not exist:

mod = sys.modules.get(module_name)
fn = mod and getattr(mod, function_name, None)