Path of Exile How Does Crystalized Omniscience Work?

I Have a question. I am currently playing a champion with exploding arrows. Therefore my main bossing damage comes from the ignite of exploding arrow. I wanted to ask 2 things:
1) I was confused since you said penetration does not work on damage over time, but in many guide for exploding arrow it is stated that you should go for elemental equilibrium, which reduces the elemental resistances of enemies by 25 (if you have for example lightning damage on your normal shots) the equilibrium will reduce enemy resistances to cold and fire by 25%. I Thought penetration is essentially also a reduction of enemy resistances therefore I am a little well I don´t get it basically. Or is the reduction to elemental resistances different, and you only receive pen directly on the hit damage but it does not "stay on the target and is therefore useless for all ignite/dot damage?

2)If the pen is useless for the dot damage, will it at least increase the damage of the burning arrow projectiles. I mean probably not because those don´t deal fire damage but at the moment i am really a little bit confused.

I'm playing a cwdt scion and having a blast

I was planning on recreating the fan favourite crackling lance assassins with inpulsa and storms gift with omni, but honestly, I dunno if I can shoehorn omni in there or is it just better to go with 2 void batteries. at least if not for batteries, then annihilating light could be a solid choise for weapon too, making it far easier with the tree when I don't need to stack up power charges.
then again, just like every league, I get too attached to my first character and any alts I make hover somewhere between I plan to do them, to level 80. kinda the reverse reroll problem, where I don't want to reroll a new character cos I already have this one good level 97 saboteur that has 3m awakener dps (under ideal, but very much possible conditions) that is super pleasant to play cos clear is also nice, not to mention full immunity to curses, chill, freeze, ignite, shock, poison, corrupted blood, maim and hinder…. Like, I can just roll my face on keyboard and right about everything else except uber elder and a few other even harder content is just childs play, and I still have my target for a few upgrades over my gear too…

ill maybe give it a try on a DD build

I am definitely interested in what build you are using.