That is not how it works. Once you have done a difficulty it is removed from the pool for the higher ones. So if you do LFR first then heroic. The heroic kill will only add on the normal kill.
Nope. If you do lfr first then do normal, you get 2 embers. one that only affects LFR and the other will only affect normal. If you do normal first, it will affect LFR.
Doing LFR > normal > heroic does nothing to better your chances during that week.
Each difficulty has its own base % chance and the greater embers only affect the difficulty you got it from and those you have not done (provided they are lower difficulties). I think you need to reread the blue post Blizzard posted about this.
This refers to each difficulty having their own base drop chance. With LFR having the lowest and mythic having the highest.
Refers to how completing higher difficulties first includes the chances from all uncompleted lower difficulties for that week. Meaning if you do heroic first, normal and LFR are included.
Refers to how consuming a heroic greater ember will also apply the greater embers towards LFR and Normal provided they have not been completed that week for example