I think this can be addressed in a similar way to how theists respond to the Problem of Evil objection against the existence of God: how can a perfectly loving, omnipotent and omniscient God allow evil to exist in His creation? One common response is that God has allowed evil to exist because He probably has good reasons for doing so. So, if God has good reasons for allowing evil to exist in His perfectly designed Creation, why wouldn't God also have good reasons for allowing errors to exist in His perfectly inspired Sacred Scriptures?
Now, responding to your specific requests and questions:
so a valid answer should include a short definitional statement describing "inspired" as well as one regarding "inerrant" if it is taken differently.
Inspired: God intervenes in the universe by prompting one or more human beings to record statements for future generations to read. The prompting might or might not explicitly enforce the recording of very specific statements word by word, and similarly, the prompting might or might not allow some noise or errors to be introduced in the process.
Inerrant: The entirety of Scripture contains 0% errors of any kind.
If the Bible is not inerrant, i.e. if it contains errors, and yet is inspired by God does this not mean that the errors are inspired?
Not necessarily, the errors might ultimately be traced back to a different cause. For example, if you believe in free will, it's possible that the errors are contingent upon mistakes freely made by human beings, thus interrupting the causal chain towards God. Why would God allow this? Perhaps for the same reasons that He has allowed evil to exist.
How and why would God inspire error without being deceptive or fallible?
This question presupposes that God inspired the error, which is not necessarily the case (see the answer to your previous question). However, replacing inspire with allow, the answer would be: in the same way and for the same reasons that God allows evil to exist in the world without that being an excuse for atheists to claim that God is "deceiving" them by supposedly "making them believe" that He doesn't exist.
Without an inspired and inerrant listing of Biblical error, how can one reliably discern Biblical error and should one make the effort if the error is inspired?
I presume the most reliable method would be for God Himself to assist the believer in doing the discerning, or to directly guide the believer so they can arrive at the right interpretation.