as far as my testing went it it should be that the initiative of both teams goes down to the average.
so for example:

one player with 3 characters on refine lvl 4 and one on 6 will be slower than someone with all on 5
( on all positions ) in survival when his position 1 should be faster in normal pvp

but sadly my testing is not very accurate ... since i had to get "rid" of 2000 initiative to make 1 oponent faster than me ...

im sure he mean is strenghen, not refinement ^^ lol

Nah, Overmain meant the initiative of ninjas outside of team (no gear)

yah, i see

in normal pvp battle like during war and challenge
I dont understand how Ao's interruption ( move 4 ) goes before my move 1 ninja

Could be 2 ways
1) Your ninja isnt using a prompt skill (almost certainly not since you put in move 1, but have to say just in case hehe)
2) There's a timing window for prompt skills to be cast after the current standard attack animation. If he clicked his first, and you clicked your skill in the next window, then he would skill first since your skill would only happen after the next standard attack animation.

With regards to the OP, best way to compare initiative to plan your round 2 moves is to just see who moves first in round 1 with their standard attack. Especially if your opponent has an interrupt/acu chase, and a higher initiative, dont just cast at the start at round 2, wait for him to move then adjust your tactics accordingly, since you wouldnt be skilling first anyway. (unless ofcourse you're able to gain a positional advantage by say, controlling his position 1 ninja to leave your position 1 with a free first hit attempt)

I think that if your amount of stars is higher your initiative is higher. True. check.