It's innate. We know because other animals have empathy and a sense of fairness, both required for any workable system of morality. There was an experiment with monkeys. A monkey alone will accept either cucumber or grapes as a treat, even though they always prefer grapes when given a choice. However in pairs of monkeys if a monkey sees the other monkey get grapes and you give it cucumbers, you better duck because that monkey will throw those vegetables at your head.

I hate to say this but history tells us that morality is very much a shifting sand. What is morally abohant in one generation can be perfectly acceptable to an other and vice versa. Take for example language. You may use the " F " word quite freely now. I even heard it used in the new star trek netflix production. However it is not acceptable to use the " N " word. The age of consent can vary from generation or even US states. I was shocked to discover that my maternal grandmother was married at 12! Slavery was perfectly moral 200 years ago, homosexuality is still seen by some as immoral but the tide is turning. Yet in ancient Greece or Rome it assumed that you were at least bi. In Spata it was compulsory. Yet when Oscar Wilde was sentenced the judge said that it was the worst case he had ever tried and his previous case had been a child murderer. Who knows maybe future generations will look at us as inhumane bastards for eating meat or owning pets?

No, there's no universal morality.

Also, that value of life argument will only hold true for so long. Once the decision changes from should we let this person live or die' to 'should we let this person live or that person live' we'll be no different than any other animal.

Life based universal morality fits the dichotomy of man being good and altruistic or bad and self serving. I prefer the former and consider the darker side of humanity to be learned behavior. Religion is not morality, nor is it a good basis for morality. Obedience to a deity or unquestioned faith in a spiritual movement seem to shade things and allow for immoral behavior in the name of the subject religion.

Do no harm. Period.

No. Morality is relative.

I don't believe there is a universal morality. If the majority of our population were serial killers and they made the rules, then it would be "normal". It's whatever the majority is that takes precedence. It's possible there is a society our there in this universe or the next where murdering people is legal etc. This kind of goes back to evolution. Evolution doesn't care about morality. If Hitler would have succeeded then he would have constructed a society in which each new generation was taught to believe what he believed. Soon, they would have outnumbered those that opposed those beliefs and thinking otherwise would be looked down upon as being immoral. Laws they could make would be in favor of them and disfavor others. Why? Because they are the majority rule and the "norm". Just look at different societies in our own world. In Saudi Arabia it's normal to chop off the hands of thieves or honor kill women who are raped or kill gay people or chop off the heads of non-believers etc etc etc. We don't have the same morals in the U.S. for the most part. There is no universal morality.

Yes to there "being" a universal morality. The one basic tenet: Do nothing that destroys or severely damages individuals. The real bottom line, anything that de/limits potential reproduction. Otherwise, the remainder (vast majority) of morality, ethics are culture/cultural... patterns of learned behavior. Nurture, not nature.

I think there is a universal morality, but like a Wikipedia page, it is written and rewritten based on what the current captors of moral attention see as being appropriate. Morality is a rather primitive concept, in lieu of a more empirical system of understanding human behavior, we have developed a system based on the idea that each person has the ability to manage their "morals", and can be born as "morally good, or evil". this was relevant in the initial age of the war on drugs, where the main source of reasoning towards addiction to a substance was morality. it wasn't a problem that you used a drug, but the addiction to it that made you immoral. in the modern age we now know through testing, that genetics and environment play a large factor in the development of addictive behaviors.

The higher primates including man have mirror neurons in our brains that mean we experience an attenuated version of what we see. Easiest example of that is watch a bunch of men when they see someone else get hit in the nuts. So empathy is inbuilt.
From that comes the fact that if you cause someone else suffering you experience a milder form of it yourself. What sane person is then going to inflict suffering on other beings. Now days of course technology allows us to do so at a distance thereby circumventing that response but we as rational creatures are still aware of the effect of our actions. We try to convince ourselves they are not like us to break the link, but for most people we really don't believe it.
So the desire not to cause suffering informs our morality and for most of us is inescapable.

There are universal truths. For example, there is no modern culture that condones child sacrifice anymore - it is universally wrong. Also, every culture has concepts of justice, beauty, and the like, although the specifics of each may differ; so you may consider those universal as well.

There are universal mores across cultures. Murder, un-sanctioned killing, is universally condemned. Look into cross cultural anthropology.

I think there is a sort of universal morality baked into us by evolution. Evolution is what made us so everything we are and do comes from it. Many think that morality comes from religion but I think the reverse; religion comes from morality. It is our nature to be moral (among other things) and that manifests differently in different cultures and at different times as religious as well as non-religious behavior. There is really no useful distinction between religious and non-religious morality. One is described in poetry; the other in prose.