Factors influencing patentability

Answering the second part first - Almost all patents can be thought of as improvements on something that already existed. One gets a patent for developing a new, useful and non-obvious invention regardless of ownership of any other earlier invention. You can get a patent on an improved razor blade without having any rights to make the underlying original razor blade.

Patent owners can use a granted patent to try to stop others from making, selling, offering for sale, importing or using their invention but a patent does not give the patent owner any positive rights. That means having a patent only can prevent others from doing something - it does not have anything to do with allowing the patentee to actually make or sell the invention themselves. It may be that there are other patents that would be infringed by the patentee making their device.

In terms of degree of change from what already existed, it is not the size of the change it is the obviousness of the change. A small change can have a big and unpredicted effect and be the subject of a patent.

The first part of the question is really two questions. To get a patent the invention must be new. If "unique" means new, then it must be completely unique. No - it can't be vague. What mails down the scope of a patent is its claims. Claim wording must delineate the invention so that someone skilled in the art can know what is and what is not covered. A claim can be general/broad if the ideas behind the invention are pioneering. This is not usually the case.