I can, of course, only speak for our airline:
1.
The yoke-checklist is company-tailored (as in most airlines) and therefore totally agrees with the hand-held (which is also company-tailored).
2.
To obtain the original (Boeing) text, you'd have to find an airline that uses original Boeing procedures.
3.
This checklist is done and read when cleared to enter the active runway (not when cleared for takeoff at our company). It provides ignition to the selected igniter. This reduces the probability of flameout during takeoff (and landing, where they are also selected on) under unvafourable conditions like strong, gusty crosswinds or heavy rain.