Guild Wars 2

Introductory Paragraph:
Hi guys,
I’ve broken up my questions into three relevant sections.

1. I ask about the damage mechanics of mainhand/offhand weapons.
2. I ask about mainhand/offhand sigils.
3. My own personal problem with sigils and offhandedness.

Questions on Damage:
Can someone please explain to me how mainhand + offhand stats contribute to your damage. Do both weapons contribute to your overall damage, or only the weaponskill it is tied to?
For example: The mainhand stats contribute towards skills: 1, 2, 3
The offhand stats contribute towards skills: 4, 5
If so, how do dual skills work for Thieves? Because many of the dual skills involve striking with the offhand weapon in the combo before the mainhand weapon.

Questions on Sigils:
How do sigils work in terms of Mainhand + Offhand? I have heard that if you have two sigils of the same approximate type – i.e Sigil of Fire and Sigil of Air – that the game rolls and checks for the mainhand sigil first.
I have also heard that if the sigils are of the same type (as with previous example), that IF either of the sigils are triggered, the cooldown is the same for both of them. Is this true?

My Dilemna:
What I want to do with Sigils, is to put a Sigil of Energy on my mainhand sword and a Sigil of Fire into an offhand sword. Since these are different sigils with different cooldowns, will this functionally work the same way as if I put the Sigil of Fire onto my Sword and the Sigil of Energy onto my Dagger?
I’m just concerned that the Sigil of Fire won’t trigger on my 1, 2, 3 attack skills since I put the sigil of fire onto my offhand weapon.

Thanks a lot for reading this walltext!
I’m looking forward to the responses!

1. As far as I know both weapons contribute to overall damage – your skills are affected by your total stats and not the weapon they’re associated to. (Which is why 2handed weapons have higher stats, to contribute as much to the total as 2 x1hand weapons).

2. Any pair of sigil that are not the exact same should have their own separate cooldowns, even if they work in similar ways like Fire+Air. I am unsure if there is any priority, but the wiki at least says there isn’t.

The only exception I’m aware of regarding sigils conflicting with one another is stacking sigils, in whose case the mainhand does have priority.

3. The functionality should be the same whichever way you put the sigils, and the Fire effect should be able to trigger with mainhand weapon attacks even if it’s on your offhand.

1.
Stats like Strength, Precision, Ferocity work on all skills.
Weapon strength works only for the skills you use with that weapon.