Noachides are not commanded to keep Kosher but we do know the sixth commandment given us is "The prohibition of eating flesh taken from an animal while it is still alive" can someone clarify (Not give an official word or ruling) how we can best observe this commandment? My wife and I rarely eat meat due to the inhumane way the animals are treated and obvious other reasons like horomones and the like. In a community where we have no shochet to teach us to kill our own meat righteously and no place to buy meats like this is it best to be vegetarian? Also are we supposed to observer the law of not mixing meats and dairy or are we allowed?
Your first question should be asked of somone who is an expert in animal slaughter such as the OU or the STAR-K (Baltimore Vaad Hakashrus) who can tell you if the 'humane' practices required by the FDA ensure that the meat is not 'living' when it is being cut up originally. It could be a matter of how long after the slaughter they wait to actually cut it into salable portions.
As far as your second question, I would say that you are no more required to separate meat and milk than you are required (by Noachide law) to refrain from eating pork or shell fish. In fact, the Talmud actually gives the fact that nonJews are allowed (and do not suffer ill health) in order to show that the laws of Kashrut were not given for 'health reasons'.
Vegetarianism for health reasons (such as hormones) as an example is completely permissible, while vegetarianism for the purpose of treating animals 'like humans' (such as PETA) is often thought to be a form of idol worship.
In any case, a diet of this type should be checked with a doctor who is an expert in nutrition, to ensure that your health does not suffer. There are people who went overboard and caused malnutrition by not being careful.
You can also find a number of answers to your first question at Are there any hechshers that certify food as kosher for B'nei Noach?
Source 2 has “Recommended practice” (source: Dr. Temple Grandin) which states that Cardiac arrest stunning is more effective than conventional electric stunning. This may give a guideline on how to shop for meat.
Sabahillel already answered your question on meat and milk.
As a Noahide, I understand scientifically that an unclean animal has two veins that runs to its brain (like a pig or horse). So that means even if you kill the animal the kosher way by cutting the one vein beneath its throat, it is bound to feel pain because blood will still be flowing through the other vein to its brain! In the clean animals they only have one central vein passage that goes to the brain. So as you kill them you immediately causes the brain to die and hence no pain sensations!
Therefore, I can't agree with any Rabbi who says it is Ok for a Noahide to eat unclean foods like a pig. Because logically if the unclean animal feels pain when you slaughter it, that amounts to TORTURING THE ANIMAL! That is just like taking its limb whilst it is alive!
So yes ... yes indeed, I firmly believe a Noahide SHOULD NOT EAT an unclean animal! It is violating one of the 7 Laws of Noah because the unclean animal feels pain before it dies even if you slaughter it the kosher way!
Moreover, I will go as far to say, any CLEAN ANIMAL not slaughtered the Kosher way (such as in the slaughter houses in America, etc ...), is TORTURING the animal. They die in fear, and anyone who eats them, eats "the fear"!
By the way, didn't G-d told Noah they entered in the Ark to separate the CLEAN from UNCLEAN animals ??? That would mean clearly that Noah MUST have had a knowledge of what was clean and unclean foods!
Reg "The prohibition of eating flesh ... " this it is not exactly the 6th law, but the seven (the last one) because it was commanded for the first time to Noah by HaShem Itself after the flood . ( In Tanach it is wrote : " But flesh with its soul its blood you shall not eat " Genesis/Bereshit 9:4). The other 6 were given already to Adam in the Garden of Eden. The Noahide laws are an Universal Code for Morality which must be respected by All the Humanity . Moreover , should be considered that this 7th law, regards the sexual promiscuity too . Reading and studying this laws only with a " strictly literal " eye it's not enough. There are many concealed significances and the work to do is only at the beginning. Torah is the wisdom of HaShem , and His Wisdom is Infinite . Be well and prosper . Shalom v'Brachot !