1.) When a special power say that the character has outwit and perplex does that mean that the character can use perplex first, then outwit and he wouldnt miss the effect of one or the other by using them both on the same turn?

Ex. The new darkseid uses MASTER STRATEGIST on the icons superman to outwit his impervous then uses Perplex to reduse his defence. would the outwit I did first still apply after the perplex?

In short, yes. To all.

Just to note - Darkseid in question doesn't have an SP that say he has both Perplex and Outwit, it says that he can use both Perplex and Outwit. That wording can make a difference in some cases.

You could also put Brillant Tactician on him since he "can use" both Perplex and Outwit. Which could give you a cool advantage for that Apokalips/Ruler theme team. If you was in a large point build you could have the Unique Superman from Cosmic Justice doing 8 or 7 clicks of Damage rolling a 12 or 13 depending on your use of the Perplex. But you'll need a couple Parademons Scout/Warrior to fill out a 500 point Theme team which point value range from 13 to 25 points per.

Or even better a Ruler theme team with an endless amount of options there.

Good luck

Or 129 options (128 technically since you want to commit to Darkseid)

The only exception is the AA Question, where the wording of the power specifically prevents this:
So Question needs to choose one or the other.