DoT, skill duration

Hello, I never played PoE and the only wiki page I can find refers to the first iteration of the game.
I was wondering what is currently in the game that can affect DoT damage. All that affects skill duration should apply to it and increase/decrease the damage if there is an increase/decrease to the skill duration (they tamper with the damage through the duration but do not affect the single tick damage).

But are there yet the modifiers that amplify specifically DoT damage?

The wiki page also mentioned that modifiers to spell damage affect only DoT of spells specifically stating this (contagion, essence drain), but do modifiers to chaos damage apply to the mentioned skills as well (because they do chaos damage)?
Like, also increased fire damage would increase ignition damage?

Yes chaos damage will scale DoT like spell damage. Skill effect duration will effect the duration. Withered applies 5% more chaos damage per stack which scale chaos DoT also.

If you examine the advanced tooltips of things like essence drain and contagion for example it will say

"Modifiers to spell damage apply to damage over time caused by this skill" or something close to that, so spell damage directly buffs dot damage on spells