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 my answer above to your previous question). However, if we replace 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. Christians assert that the Creation points toward the Creator (the teleological argument). Atheists claim that all the evil and suffering in the world points toward the inexistence of a loving Creator (the argument from evil). If God can allow evil and suffering without being deceptive (thus invalidating the atheist's complaints), why can't God allow error without being deceptive (thus invalidating the inerrantist's complaints)?
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?
Ignoring the fact that this question presupposes yet again a questionable "if the error is inspired" (see answers to specific questions above), 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 towards the right interpretation.
Note: Entertaining the idea of God inspiring errors is analogous to entertaining the idea of God causing people to sin. God doesn't force people to sin, and yet people might still sin. In a similar manner, God doesn't inspire errors, and yet errors might still occur. But it is true that God is overseeing the whole process in both cases, and only allowing them to happen within certain boundaries such that His purposes are still fulfilled.