I don’t really know where the question is going. Let’s try to structure things a bit.
- In pure model building terms, you can put everything you want into a feedback rule. The only limit is your imagination.
- When it comes to the describing actual policies/central bank behavior, things will be different, because central banks may care about very specific things (which will typically differ across countries and time)
- Things are again different when doing a normative analysis, i.e. whether feedback rules should respond to particular variables. Here, the answer is not a priori clear.
Regarding your last question: every shock you put into the monetary policy rule will be isomorphic to a monetary policy shock. But you may give it a different interpretation, e.g. anticipated shocks may be forward guidance shocks. What is usually not feasible is having the shocks represent endogenous variables as they are exogenous objects.