What is the nature of value?

Are you asking the question meaning 'principles' or 'standards' such as issues of morality?

Or are you asking the question to understand value, such as 'value in use' or 'utility'?

I see that some of your questions would be applicable to both. I am going to assume here that you are looking for what the sages have described as "right living". Therefore your question may have been better understood if it were rephrased to something like; "What is the nature of morality?" Since I believe you are working towards 'moral values'.

The history of philosophy is filled with discussions on this very subject. So I will attempt to answer your questions specifically.

1) are they meaningless? No. Any amount of morality promotes consistency and reduces repetitive work.

2) are they relative? in a sense yes, but more accurately no. And this is based on the functional truthfulness of the moral in question. An eternal truth is true regardless of person or cultural context. An ancient would say "right living" is right regardless of creed.

3) are there things we should all value? Yes. And this becomes subjective. We should value our existence. And how we value it becomes relative to our knowledge, wisdom, and understanding and recognition of eternal truth.

4) should we value nothing? Does this mean; should we not have principles or standards or morals? Without them we would have destroyed ourselves long ago.

5) do principles and standards exist regardless if people recognize them? Yes. Once again that which is described as "right living" exists regardless of individual belief or acceptance.

6) is it possible to have opposite standards, principles or morals and both sides still be correct? No. Since what is right will be right and what is wrong will be wrong.

Now the last one from a standpoint of 'value derived through utility' the answer could be yes. For example say I liked apples and you did not, in fact you are deathly allergic. We would be opposite, and both be correct based on the utility the fruit provided. Useful to me, but not to you. Positive for me, negative for you.

The biggest problem with getting the right answer is in asking the right question. I hope this has been a little helpful.

Value is up to the eye of the individual valuer...

It's never meaningless to the individual.

A culture may have values, but it is because it is made of the composition of many indivuduals values.

You can value nothing, if you want. But chances are you will never be able to remove all personal value in your life. Suiciders even values the release to death.

Value's only exist in your head. But are important in social interactions. Opposite values can be understood by another person.

For example, Japanese in WW2 saw that is was a value to commit suicide before dying to the enemy, where westerners believe fighting to the last breath is honorable. But as a westerner, I can understand the japanese point of view.