Hi,

I know there's the strong attack, pressing down left and right mouse at the same time. But during a fight this isn't always that easy. So I prefer using this while being behind an enemy.

Can you recommend using this strong attack during a combat?

There are some perks that give +speed or +attackpower for dual wielding (Dual Flurry for example). Does this mean, that it only works when having two weapons equipped, or does this mean it gives +speed/+power when triggering both mouse-button?

Hold them down. Don't just press them at the same time. http://www.uesp.net/wiki/Skyrim:Dual_Flurry#Dual_Flurry should clear up some confusion. If it says power attack, then it only works when power attacking, and if it says just "attack," then it will work as long as you have two weapons equipped.

The fully Perked Dual Wielding Power Attack is the greatest DPS attack in the game, and the ability to strike at an opponent with Four Enchants at the same time is only possible with it.
Dual Wielding is my second favorite Melee playstyle, behind using Two Handers. The playstyle is very effective, but performing a Power Atack means being stuck in one place until the attack is done. I have been unlucky enough to suffer Killcams from Draugr, and a few ordinary Bandits.

I have taken out a specific Frost Troll using Dual Wielding at level 6 without getting hit once, but My character was built to use Dual Bound Swords and got lucky, because I tried to repeat the fight, and usually had to drink Potions.