Curiosity is the quest for knowledge or information. Perhaps for us, with our intelligence, it is also the quest for wisdom. However we’re not the only ones who are curious, most life forms that have a brain and the capability to remember things to varying degrees, are curious.
Curiosity is vital to survival. It’s curiosity that makes you go out to find good places as food sources. Mobile life forms (mammals, insects, birds etc) use curiosity to find sources of food. Curiosity allows you find better ways of doing things. We’re not the only tool users there are a few other species who, through curiosity, find better ways to hunt or obtain food. Curiosity helps us find more effective ways to defend ourselves too. This is a quality that aids significantly in the survival of a species.
With regard to your questions …
1) I tried to answer above in terms of what curiosity is.
2) It is always good to be curious especially for us, for through curiosity we gain more skills, knowledge and wisdom. However curiosity has to be tempered with caution. Sometimes that which we happen to be curious about could be dangerous to our well being. It is not good to be curious without also being cautious.
3) I don’t understand your third question.
4) People, and most species with a brain are naturally curious, it’s built into the genes. So yes, curiosity is an inherent quality we are all born with. The problem with it is that if we allow it to go unchecked we may not survive long enough to learn anything so it’s important that as it grows we also grow caution. That’s why fear is another quality we are born with.
5) All people start with being curious, not all people remain really curious. If you’ve even had a child that keeps asking “Why” you can become very very frustrated in a short period of time because each subsequent “why” leads to an ever more profound question, eventually the tendency among many adults is to get so frustrated that they will admonish the kid to the point where the kid gets the message that being curious is not a good thing. The curiosity doesn’t die in that process, but it can be stifled so much that it becomes virtually useless.
6) Yes, peoples should be curious and if more were actively curious we’d live in a much better world because we’d tend to question more things and seek ever more wisdom in the process.
7) It’s a warning that you need to be careful. Cats are either sniffers or touchers. When a cat gets curious, and they all do, it will either examine the new thing initially with its nose to see if it smells safe or it examines it with a paw. The touchers are wiser because it keeps the animal back from the object and if something goes wrong it can pull back with minimal injury. A sniffer can ‘t pull back as easily without harm. I suppose a lot of cats, especially sniffers, probably have been killed because of their curiosity. But where the deaths most likely occur are in the young. It’s the young of a species where curiosity is really strong because it’s an excellent motivator to learn and gain experience, but at the same time young lack the wisdom and experience to be cautious and so are at the greatest risk.
8) Being curious means to have a need and a passion to explore things with a view to better understanding them and gaining ever more skills, knowledge and wisdom.
I hope this helps a little.