> I have no idea if smalltalk can do this,
It can.
> if my examples are good examples of showcasing the automated refactoring problem
They're not.
More to the point: Smalltalk is as dynamic a language as practically possible and was like that for two decades before Python existed. The `__getattr__` from Python, `method_missing` from Ruby, and `__index` from Lua are all inspired by Smalltalk's `doesNotUnderstand`. The concepts of metaclasses and first-class message sends was invented in Smalltalk. The idea of inspecting code using a GUI instead of flat text files also originates with Smalltalk. Refactoring, as noted by GP, also came out of Smalltalk-land. Smalltalk gives you all that without any static typing in sight.
How? Smalltalk is special. Normally, you have your code: a static blueprint of what's going to happen; and a program: part of computer memory which your code gets loaded into and gets executed. This is true for both statically and dynamically typed languages: the familiar type something -> hit "Run" -> see if it worked cycle works equally well in Java and in Python.
Smalltalk is not like this. With Smalltalk, all you have is a program. It's always running. You hand it the code and it patches itself dynamically in memory. The classes are live objects you can query. Metaclasses are, too, objects you can query. They implement methods for refactoring. It's easy, because there's no need for any parsing, statical analysis of any kind: you just iterate over all the classes in your system and ask them one by one: "do you call such-and-such method?" And the classes inspect themselves and say: "why, yes, I call it when handling such-and-such messages, here's the list".
Really, Smalltalk is special. It's not unique: Forth and Common Lisp come to mind, Self, Lua and Io too. But it's special and very few modern languages come close to its capabilities.