2 phase = bipolar, 4 phase = unipolar. The EasyDriver is for bipolar motors only. "2A/phase" is the peak power it will use but average power is slightly less. Moot point because it's clear that your motor and driver are not compatible anyway.
A 2S LiPo is (3.7V * 2) = 7.4V and a 3S LiPo is (3.7V * 3) 11.1V nominal. Either a 2S or 3S is acceptable (a higher voltage battery allows you to move the stepper at higher RPMs) but you need to look for the mah (milliamp hour) rating to know how long it will last.
If you're looking for a baseline build take a look at this MakerSlide Camera Slider. He's using a NEMA 17 size bipolar motor, an A4988-based stepper driver, and a 3S, 3000mah battery. A 3000mah battery should be able to run something like this for a full workday.