The par value of $0.0001 per share has nothing to do with the price you will pay to exercise the option. Technically it says your option price cannot be lower than that amount, but realistically it will be higher. How much higher depends on the value of the company’s stock at the time the option is granted. For a company whose stock is not publicly traded, the value is determined by the Board based on various factors, including the value of the company implied by the most recent round of funding.
Even if the description you were offered did not indicate an expiration date, you should expect that the option will expire after a specified period, which is often ten years but may be less. The option will most likely terminate early upon the occurrence of certain events, such as a change in control of the company.