Can't speak for Aurino, but I'll give you my take:
***Is mathematics a human invention, or does it transcend mere mortal cognition? Did we invent "sqrt-2", or has "sqrt-2" been around since the universe was in its infancy, simply waiting around to be discovered by mathematicaly estute consciousness?***
The ontological answer is outside the grasp of thought. That is, we use human logic in order to broach the subject matter, yet philosophers cannot agree whether logic is a subset of math or math is a subset of logic. Hence, answering your question may require that we assume math in order to decide if math exists. Not a very firm starting point if you ask me.
On the other hand, the world cannot even be dealt with in any meaningful manner without assuming our logic exists (and even mathematics exists). If logic does not exist, then nothing and everything exists. That's not how we approach our lives, nor could we approach our lives that way with any consistency.
Therefore, for purposes of our lives, we must treat mathematics as existing. If it doesn't, then it doesn't. We can't live any other way (or at least we shouldn't try to live our lives any other way to remain consistent).
***Is God a human invention, or is there something greater and omnipotent "out-there"***?
I'm going to repeat what I just said, but the added twist is that some human inventions must be treated as existing since those are critical human inventions providing essential meaning to human beings. God is such an 'invention'. So is the 'family'. So is 'love'. So is 'morality'. Without treating these 'inventions' as real, life loses meaning and we cannot function in our world with any degree of effectiveness or happiness over large spanses of time (at a societal level).
***Is a chair a human invention, or did we simply discover a concept that has forever existed independent of human consciousness (or any alien consciousness for that matter) and then mold it into its physical manifest via manipulation of matter.***
Another human invented concept with a similar answer as before. Fortunately, as we start thinking in more and more abstract terms, the essential meaning imputed by the concept is no longer necessary for many to believe or even know about to lead meaningful lives. For example, the average Joe doesn't know what a quark is, and they don't have to know or know whether it exists or not. A particle physicist, on the hand, must hold some form of the quark theory as 'existing' and 'true', otherwise physics can start to become meaningless - thereby threatening their profession. So, there is nothing wrong for a physicist to look at someone quite strangely if the other person questions whether quarks exist. For the physicist, quarks are meaningful concepts and treating them as existing is normal and healthy. That doesn't mean that a physicist should be ontologically committed to the quark existing in the coneptual form that it is currently conceived. It only means that a physicist can and probably should be ontologically committed to a quarks existence within the bounderies of our theoretical conceptions as they are currently formulated.
***Does right and wrong exist?***
Yes, in the sense mentioned above.
***If it exists now, did it exist 3 million years ago (or were we released from all liability pertaining to our actions, seeing as how we were lowly apes)?***
Yes, it existed, but in an entirely different sense as it was conceived of by those creatures. Whether all of these differing moralities throughout the ages exist in some pure form 'out there' is beyond thought. Although, we are bound at some point, I think, to believing the statement that 'morality exists' is true.
***If two cultures disagree on homosexuality, does right and wrong then become relative concepts? Can both cultures be "right" in their beliefs so long as they "stay on their side of the white line"***.
It depends on how meaning in their lives is functioning with or without the belief. If culture A has a religion that forbids practicing homosexuality, and culture B has a religion that requires it as part of their religion, then it is 'right' in one culture and 'wrong' in the other. Is there an ontological 'right' or an ontological 'wrong' here? Again, it is beyond our ability to know. We can treat it as ontologically right or ontologically wrong, but that depends on us and our frame of reference to such matters. So, you have to ask yourself the question. Does life becoming meaningless for you if you think it is okay to practice it? Do you think God would allow it? Are you convicted to a particular interpretation of the Bible, for example? If you feel life is more meaningful rejecting the practices, then by all means you are free to believe and treat homosexual practices as morally wrong. However, as a society, we cannot just decide such issues based on your needs and wants, we have to decide based on societies' needs and wants. In a democratic society the path of those decisions is different than other societies, but each society has their way of enforcing their set of meaning onto the minority. Had this been a Muslim country, no doubt that lady in Florida would have been able to keep her veil on for her driver's license picture. But, our society holds a different set of meaningful concepts, and therefore the court ruled in favor of how our society holds those particular concepts. Is it 'right' that we do that? From our particular perspective and the things we treat as our ontologically commitments, I think is 'right'. Is it 'right' in the truest sense of the term? It depends I guess on whether God is a Muslim or not.
***Is the use of controlled substances wrong in the U.S. but right in Holland?***
Allowance by a culture laws does not necessarily mean that it is 'okay' to engage in illicit or immoral acts. One should be consistent in their morality from a set of first principles (e.g., God exists, God demands that we take care of our bodies, etc). If the set of first principles are truly meaningful and do not lead to addictive behavior (which is a very unmeaningful lifestyle or the result of too much meaningless in one's life), then an action can be 'wrong' despite what laws are on the books. The laws should be changed for that society.
***Can a childs actions be "wrong" if he was never taught what not-to-do?***
As a child progresses in life, the child is under the domain of the parents' moral choices, and it is 'wrong' for a child to do actions that violate that morality since the child is under your domain. As the child ages the child comes less and less under the domain of the parent, and the child who becomes a teenager then young adult must develop their own set of 'rights' and 'wrongs' within the context of their family and society and world around them, and the cycle repeats itself. If the child is never taught the morality of parents, extended family, society, then the child might start to experience the effects of meaninglessness in their lives, and this is the result of violating 'right' and 'wrong' behaviors - even if the child didn't know the 'rights' and 'wrongs' to avoid.
***Is right and wrong black & white, or many shades of blurry grey?...***
In some cases it is right and wrong, and in some cases many shades of blurry gray depending on the circumstances and a person's temperment, etc. Meaning is what we seek in life. If that is in anyway threatened, we must add the necessary moral hardware to our lives to protect us from a meaningless period in our lives. This might mean changing lifestyles (e.g., going to church, start exercising, debating on the internet, etc).