When they count the speed aura and they are the same speed, the champion with the higher base speed will go first due to recieving the aura.
Likewise, if two champions have the exact same speed counting aura, sets, buffs, and masteries, then the champion in the higher position will go first.
Higher Accuracy means a greater chance of landing your debuff, so you always want your accuracy have a good gap between the enemies resistance.
Even if you have higher Accuracy, your devuffs still can be resisted. Put as much distance between the enemy's Resistance as possible.
Lastly, even if you have 1000 Accuracy and the opponent has 0 Resistance, there is always a 3% base chance of an enemy resisting a debuff.
To add, High Khatun has a base speed of 104, while Elhain has a base speed of 107. The speed aura applies to the base speed of the champion. This means that even if both of these champions had the same speed prior to battle, the speed aura would be different for both.
For example, assuming you are using HK's speed aura of 19%:
HK's base speed of 104 * 19% = +19.76 speed to her total speed in the game
Elhain base speed of 107 * 19% = +20.33 speed to her total speed in the game