Assuming I have a customized skill kit, in some cases if I don't know how to handle users' questions, can I redirect it back to Alexa's built-in skills? If I can, how can I implement that? Any hints are very appreciated!
No. You have no access to functions built into The Echo. Alexa has no built in functions. It is just a service. Similarly The Echo does not come with skills. The functionality it adds are at a base level, not through the same interface the rest of us second class citizens have to go through. I think when you look into skill development a bit more, you will find few points where this matters. Since you have to very precisely define the interface to your skill, you can define exactly what you can handle. Basically, it's hard for the user to send you something you don't know how to deal with.