How about I try this question another way. If I were to make a people who were half Dragon and half Human, What would be some of their traits and characteristics, as in what are the traits and Characteristics of a fire breathing dragon, frost dragon and so forth. My concept I am doing is to have them be humanoid in form. And their only defining trait in the eyes. Like the movie pitch black. But can someone explain to me dragon behavior, how they interact with each other, how they interact with other races, is there a hierarchy, do they eat their young, do they share? Basically those kind of answers.
Focusing only on your first question, "what kind of powers would dragon people possess?"...
Let's take the major attributes of classic dragons as a starting point. They have wings, scales, and claws; keen-senses and fire-breath; and most useful to their evolutionary descendants, great age. Dragons live a very long time.
Now assuming that a humanoid race somehow arose from the base material of dragons, we would expect them to have all of those attributes, only in smaller scale and potency.
Dragon wings scaled down proportionally for a human size body would be smaller than is commonly portrayed. After all, the Dragon scale versions of these wings can lift not only a dragon size body but also a large quantity of gold (which is not exactly light). Let's scale the wings to arm length and make up for their lack of surface area with dragon magic. Make them work even though they shouldn't.
Dragon scales can evolve into natural body armor; very close fitting, light and tough. But permanently attached body armor can get in the way of a lot of humanoid activities, so lets add in a little dragon magic and make the scales retractable. The dragon folk's backs are always scaled but the rest of the armor appears and disappears as needed. Same with the claws. What good is it to have humanoid hands if each finger is sharp enough to cut mithril? Make the claws retractable too.
Enhanced senses are not big deal. Lots of magical races will perceive the world better than regular humans. So leave that totally unchanged since the age of the great ancestors. "We have lost much of what we once were, but we still see the world as clearly and as deeply as the great ones ever did."
Personally, I would tone down the fire breath to be a utility level talent. Let them easily start camp fires and maybe burn through wooden doors, but have them carry a little shame that their diminished human-sized lungs can no longer produce True Fire and that even the best of them can only produce a foot long breath of flame. As compensation, make them immune to fire and heat of all forms.
Age! This is where the Dragon Folk can really shine. How good at sword play could you get if you had a thousand years to practice? How many magical disciplines could you master over the course of a dozen human lifetimes? What skills would you not have, if you had all the time in the world to learn? Ancient dragon folks are insanely powerful because they've had longer than any of the rest of us to acquire and master their power.
And as a writer, age is a great kind of power to give your character's race because it doesn't immediately overwhelm the powers of your other characters. Yes, your dragon folk character may someday be more powerful than all of your other characters combined, but only if she lives that long. Right now she is a twenty-three year old dragonette with no more power than anyone else her age. She is arrogant because she knows she may someday be powerful, but only if her lust for gold and power doesn't end her life centuries before her time. She is fundamentally flawed by pride and greed, yet she possesses incredible potential.
Now that would be a fun character to write about.
It seems like you want to know if this has been done before.
You are calling them "dragon people" rather than just...dragons, so I assume that they are what? human sized?
First, take a look at D&D and establish what real dragons are. Your dragons may be completely different, but it's not a bad place to look. And the VARIETY of types is staggering and interesting.
Second, you need to ask the question about how they got to half-human half dragon, which is how you describe it. Why in the heck did they interbreed? Why is it its own race now? Was it always thus? half-human half-dragon doesn't sound that way.
In D&D Dragons can polymorph into human form and they do breed with elves, humans and the like.
Also sorcerers in Pathfinder are said to be of specific bloodlines to have specific abilities. One of which is dragon. Look that up because it's actually pretty...underpowered compared to the others. Take a look at the guide to the abilities in comparison with the other bloodlines. These are human/elf/whatever race casters that get more and more dragon-like as their abilities progress (FIRE, ICE or ACID BREATH!). The assumption is that a dragon bread with a base-race generations back while polymorphed. Somehow a child was born, which would not be possible without...magic.
You also might want to look up Dragonborn in D&D 5 (although please do not give them breasts if they look like this, which I see in fan-art all the time, because they are lizard people. They should not have mammary glands! They come from a dang egg!!)
These might not be on target with what you are doing, but they are all very very different paths to what one might call Dragon People. And as such, they might have ideas that you can look at and reshape.
I don't know if you want them born from eggs....I think there are a whole passel of questions you need answered from an evolutionary standpoint before you even get to magic.
You've got to build your species. We can't do that for you, neither is this site about generating ideas for you! But we CAN help you get the tools to build your species, and answer SPECIFIC questions about one thing making sense and what it might impact.
I suggest you start with this lovely question and the outline here and just...start answering the questions. Come back to questions if you find your answers don't make sense given your next answers. It's a great guide for building a species from the ground up, right here on this site! Mine is the chosen answer, but there are also some quite valuable answers in there that come at things from a slightly different angle.
Peculiar traits of dragons are:
- resistance to magic
- fire related stuff
- ability to fly
When you state
their power is great in numbers, but individually they are weak
you are kinda defeating the first one, and having them bearing human traits may also remove the ability to fly.
But for the rest it makes sense. They are disdained by other races, thus being half human they can disguise as normal men among men (if they don't bear peculiar traits like scales skin) and refrain from using fire magic, unless maybe for developing great forging skills.
Being smaller in size they can also better hide than a normal dragon, which, you know, once installed in a city pretty much wreck it to the last brick and really doesn't keep it a secret that it is there...
 Ask Smaug for reference