Dual Wielding mechanics in Skyrim

For you 1st question yes on hit effects occur during both normal and power attacks. As for your second question I believe that your target will be affected each time your weapon touches them so yes seperate effects will occur for each strike including "normal" swings with two weapons.

and the 2 from swinging "normally" with both your weapons at the same time?

A test: 1 iron dagger enchanted with fear, 1 iron dagger enchanted with soul drain.

I swung both weapons at the same time against a wolf.

• The first swing didn't kill it and it ran.
• The second swing (30 seconds later) killed it and the soul was drained.

Conclusion: both daggers had their effects applied both times.