Morality is a interesting character of life. In order to maintain the interest of survival, we got to have a minimum level of it, it is intuitive to have it as it is showed in animal world. If it gets below the minimum, it will be disastrous. But no one can afford too much of it unless he is not squeezed by any circumstance. Just like the role of competition in human society. Competition-Morality serves as a pair of yin&yang for us to keep balance.
Every one has his own notion of what is the minimum, but a system has a requirement of its own. The former is a self-notion developed by a specific person and often subjective, the latter is system condition to maintain developing and is objective. So If a person's notion is too far away from the system's requirement and harmful to the maintaining of the social system, there is a conflict. As for the system requirement, read the constitution as a example.
Do we have that natural ability to know right from wrong? Yes and no. It depends on the complexity of the case. The more intricacy, the more unnatural, or more difficult to know.
Even we may possess the morality naturally, it must be a hidden deep in the root, some times we may not know it dose exist and when being influenced by the environment, we may ignore its existence completely.
If the bait or some other stimulants like hate is too attractive or strong, the law, natural or man-made, may also be ignored.
Note it or not, God exists. That is not conditional. That is also why we have some common ground.
Morality have the effect of factors canceling each other, a guy may save a baby and beat a dog, how about his morality? When the case becomes more interwinded we all get lost.
Natural laws also need to be understood correctly, that is the controversial because different groups claim differently. Man-made laws are a supplement or enrichment or explanation of natural laws. If the two goes unrelated completely we will run into trouble.
We should read morality in a context. Treating ourselves is the same in treating life as a whole.