Are the draw effect and the discard effect of Disinformation Campaign simultaneous, or do they happen one after another?
For example, I have activated my Words of Wind, and I play Disinformation Campaign. Can my opponent discard the card they returned to their hand?

The draw and discard are sequential–the discard happens after the draw. So yes, if you've activated Words of Wind, your opponent will be able to discard the card they returned to their hand.