How to balance between frequency and duty cycle in this circuit?
How can I achieve the required range of frequency and duty cycle?


Don't make life hard, use an LTC6992: -



It's operating frequency can be varied between 3.81 hertz and 1 MHz. Duty cycle can be controlled (with a voltage or a potential divider) from zero to 100% with options to limit at 5% and 95%).

It works from supplies of 2.25V to 5.5V.