Diablo – Do abilities based on weapon damage take both one-handers into account

Dual-wielding does not mean you attack twice as often. There is a slight attack-speed benefit, but this is apparently being offset for you by the lower damage from the offhand weapon.

According to this thread on the forums, the formula for number of attacks per second is

((Main Hand APS*1.15) + (Off-hand APS*1.15))*1/2

Which means that if you had two identical weapons, dual-wielding would give you a 15% attack speed bonus.

The main reason to dual-wield is that you get the bonus attributes from both items. This doesn't mean much early on when attributes aren't very strong, but is a big incentive later on. However, compared to a two-handed weapon that does more DPS, there isn't a clear winner. It will mostly come down to whether you've found better one-handed weapons or two-handed, and what your preference is for faster attack versus stronger attack.

To answer the question posed in the initial question: Only if you had 0 intelligence and no other damage bonuses!

Base damage is simply weapon damage + any damage bonus from gear (+elemental damage is effectively "+damage" as far as the system is concerned).

The formula is roughly as follows

Base Damage =
        (weapon damage range + bonus damage from gear)
        × bonus from primary attribute^†
        × other class bonuses from skills.

Ability Damage =
        Base Damage (as above)
        × % Weapon Damage listed on the ability.

^†1 primary attribute = +1% bonus damage

Weapon speed doesn't come into play at all when calculating damage from abilities.

What this means is that weapon speed is balanced as a stat; either you deal more damage per hit (by picking a slower weapon), or you use more abilities (since weapon speed affects animation time). DPS is entirely useless as a comparison metric unless you're only auto-attacking.