Level downscaling will downlevel your character to the maximum allowable content level for that area.
So this will affect all your primary stats, Toughness, Vitality, Power and Precision. When you open your hero panel you'll see your main stats on the right in white, and next to them on the left you'll see your 'effective' stats in green. These are the numbers that you're going to be using. As these numbers are changed this will effect your damage, hp, crit chance, etc.
The thing with you feeling more powerful is that you still have the higher level gear. So for example, if you are lv30 you might have an amulet with +11 power. You go to a lv10 area, and fight with players who at lv10 can't even equip an amulet. Now I'm assuming, but let's say that the downscaling is a %, then your overall stats will be higher, meaning you'll be stronger at lower level because of your better gear.
You are by no means at all invincible, but you'll certainly fare a little better due to having more or better gear. The real killer is that as a higher level you will have traits and skills available which lower levels will not. You can also use your Elite skill still, if you've unlocked it. So there are some advantages to revisiting the lower level areas.
I think most people's experiences of this will be doing each of the race's starter areas once they've finished their own.
You can read more on the wiki, http://wiki.guildwars2.com/wiki/Dynamic_level_adjustment
Character level adjustments have a limit, however. The
level-adjustment system won’t let a level 1 character go head-to-head
against a level 80 character with much chance of victory—a level 80
character is still going to have more bonuses on their gear and access
to a full complement of utility and elite skills that players just
don’t have at lower levels. This is not to say that the high-level
character will one-shot the level 1 player, but they will have a clear
advantage.
http://www.arena.net/blog/mike-ferguson-on-guild-wars-2-world-vs-world
Edit
Since Jan 28th 2013, the downlevelling has changed. https://www.guildwars2.com/en-gb/news/dynamic-leveling-adjustment/
The official Guild Wars 2 Wiki has an article on damage (calculation).
Edit: I'll try to sum it up for you, as damage coming through depends on several factors.
The damage you deal can be raised if you score a critical hit: 1% crit dmg per trait point.
Condition damage can also add to the total. +10 cond dmg per trait point.
Effective damage you do is also dependent on the level difference. Then there are the mechanics of sidekicking and scaling, the Protection boon, positioning, projectile distance, ... that are all part of the complete formula.
Update:
The wiki article has since been updated, and now contains an easy to understand formula to calculate direct damage.
It is
Damage done = (weapon damage) * Power * (skill-specific coefficient) / (target's Armor)
Armor only mitigates direct damage, so condition damage and falling damage is not mitigated by armor.
Best Answer
There are various different kinds of Sigils;
As you've found, using two 'stack on kill' Sigils does not double the cap, but when duel wielding does build up the stack quicker. You cannot use two different Sigils which provide a stack of a different stat on kill, so for example you can't use a 'stack power' and 'stack precision' sigil and get the stack for each, the first one will stack and the second one will be useless until the firsts' stack is reset (via changing zone or downing). It is also probably worth noting that on kill stacking effects will remain even if you swap or unequip the weapon.
All of the other sigils do appear to stack together, so you can for example use two static +stat sigils and get the bonus that way, or have two different on weapon swap sigils and get the effect from both.
Additionally, sigils that apply a 'charge' effect will stack with sigils that provide a stack on kill, so you can could for example use a Sigil of Sancutary to gain invincibility along with a Sigil of Perception to increase your precision.
Active effects have a shared cooldown between all Sigils, so for example, triggering the cooldown on Sigil of Strength will prevent you from triggering the cooldown on Sigil of Air, but will not prevent the passive effects of other Sigils for example Sigil of Force.
In the instance that you're dual wielding like you are, the mainhand weapon Sigil will always proc before the off hand weapon Sigil.
Sigils that have a chance to trigger on critical hits will stack their chance multiplicatively, not additively - so if you're using two Major Sigils of Water (which each have a 20% chance to Heal nearby allies on Critical Hit) you will in fact have a 36% chance of triggering the effect, not 40%, by using two.
In the instance that you're using a mainhand and an offhand, Sigils that trigger off critical hits can trigger off any critical hit, regardless of whether the Sigil is in the mainhand and you've just critical hit with the off hand - provided the weapon is currently 'active' (rather than an inactive weapon waiting to be swapped to using the weapon swapping system) the effect of the Sigil can trigger.
More information about Sigils and their effects can be found on the Guild Wars 2 Wiki.