Par value is purely an accounting mechanism. It has no practical meaning in the actual public market. (It can have some tax consequences depending on the company, but it's not material to this question)
In some jurisdictions, a company must declare a "value" for its public stock, much like bonds have a "par value". It then lists that value under "common stock" on the balance sheet. Any amount above that price that the company raises when it issues public shares goes under "additional paid-in capital" on the balance sheet. A higher par value would just mean a higher "common stock" value and a lower "paid-in capital" number - the total would be the same, though.
Most companies today use a very small par value, usually because of the tax consequences (to the founders, not shareholders) mentioned above.
Considering the par value and range, why would anyone pay the price $0.001 for this stock?
It depends on what they're going to do with the stock. If the company is deeply in debt, they may have very little equity to work with, and issuing stock would be an influx of cash that would help grow the company. But it has nothing to do with the par value.