Item Stats, Passives, and Skills

I am having the hardest time deciphering how stats and modifiers are applied.

For example, I am playing a spark sorc based on Empyrean Gaming's build and wanted to play around with freeze, so used a Call of Brotherhood topaz ring which converts 120% lightning to cold and a Polcirken. I lost DPS with these rings, though I thought with all the boosts to lightning damage then converting 120% of that to cold I would gain dps. Next I started playing around with passives and swapping lightning damage boosting ones to cold, and it seemed to slightly increase. Though not consistently. I am just very confused about how and when modifiers on items are applied as well as modifiers and stats for passives and slotted skills.