Activation Priority 
For teams with 2 or more units like politis, red lilias, inferno khawazu, etc how is priority determined when multiple effects trigger at the same time?
Ex. Conqueror Lilias on the enemy team uses S3, you have red lilias and politis on your team. who goes first?
Ex. 2, Enemy Conquerer Lilias uses S3, you have Green Celine, Politis, and red Lilias. who moves first?
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This is a very good question, sadly, tho I'm sure everyone has asking themselves the same question, there is no official data on this. However that doesn't stop people from testing, and these are the results on passives (which might be incorrect at the time of this answer)
: But all that points to POSITIONING in what determines the activation order, in this way
: Back > Top > Bot > Front
With counter-attacks tho, it seems speed is still the determining factor. While some other effects really have a fixed priority: For example, Zio's extra-attack will always be last if he gets counter-attacked
.Finally, added damage, like Senya's and Rimuru's, will always stay last priority, as the game states "end of the turn" for them.
I'm actually curious on what the concrete answer for this is as well!
I've dealt with something similar to your 2nd example but instead of red Lilias the opponent was Amid. Amid goes first, Celine triggered then Politis went after Celine.
I don't know if it's still the case, but I've read that the position of your units matters ex: if Politis is in the back row, she'll proc first, if Celine is in the back row then she'll proc first. With the order for passives triggering being back>top>bottom>front.
Would love an official answer to this question though.