1.I use baseflight for my NightHawk but most people use Cleanflight
Better coding practices and introducing tests, easier to maintain and for future development. (Dominic has software development background)
Many bugs fixed from Baseflight.
Supports more flight controllers, including CC3D, CJMCU and Sparky.
Supports OneShot ESC and more than 8 RC channels.
Additional PID controllers that uses floating point arithmetic operations. (now has 3 built-in PID Controllers)
Many more features such as RGB LED strip support, Autotune, In-flight PID tuning with your radio, blackbox flight data logging etc
have a read of this: https://oscarliang.com/baseflight-cleanflight-comparison/
2.Battery size depends on what kind of flying you will be doing, e.g. 3s 1300Mah for agile flying like flips and racing or heavier 2200Mah for crusing at a medium speed will give you extra flight time. The heavier battery will make maneuverability slightly sluggish though. I use 2200Mah and about 50-70c rating
3.
Other Advice: fit a 5v buzzer to your quad which you can program to turn on if you loose signal or go off at the flick of switch on your TX