Do Hero powers and skills stack?

If I have two Hero's in the same province both with the skill to increase province income by 10% do these skills stack (so effectivley a 20% increase) or are they capped to one skill bonus per province?

This could also apply to battle bonuses if I embed my Heroes within an army.

Yes

I do not have a complete list of each skill stacking or not but by playing I noticed that skills that increases/reduces income, corruption, replenishment, stats stacks as long as conditions are met - certain skills only apply if hero is in the region or embedded into the army.

Skills that affect combat stats like ammo count, morale, melee attack etc, also stacks but will require hero to be embedded into the army, but do note that some of these stats affecting skill only affect the hero himself or certain unit type.

However I have yet to check if having two heroes casting a same active skill on a unit in battle will stack it's effect - I only confirm that damaging spells will apply regardless but unsure about buff/debuffs.

Except Hero Active

The active effect of Heroes(Empire Captain actively increasing/reducing public order) will Not stack if multiple captains are active within the some province. This applies to All Heroes active skills.

Do not confuse this with passive abilities like each Heroes' to resist/cause +2 point of corruption for being in the province, this stacks and also with the passive that can boost up to +5/+8 per Hero(except Chaos which can cause large amount of corruption).