I want to make motorized blinds with a battery; so I am not good with the calculation of these electronics; I will go with below stepper motor, driver and other items. Stepper motor will run for almost 30 rounds per day. And the wifi module will be on all day long.
Will a 2200 mAh battery be good for this project? And how long will it run with 1 charge?
I am open to suggestions like different stepper motors or drivers.
A stepper is probably not the best for that use. A DC brushed motor with a (worm drive) gearbox and limit switches would be more efficient. Steppers are not very efficient and would require current to be applied to hold it position. The worm drive gearbox resists being back driven so will hold position with no power.
ok to DC brushed motor with worm drive gearbox, but what about the time? And how long will it run with 1 charge of 2200 mah? (with altogether; motor, driver, wifi module etc)
Not sure what you mean by the time. Time of day? Use a real time clock (RTC) or if you have WiFi get the time from the network.
Impossible to answer without knowing the exact hardware, all specification and usage details. How much current does the motor draw? Does WiFi have to be active all the time? What Arduino board?
Sleeping the processor and motor driver can help a lot.