OMEGA EFFECTS:#Before Darkseid makes a ranged combat attack, you can choose any or all of the following options for the attack: 1) Darkseid's range value is halved and his line of fire ignores characters and hindering terrain; 2) Modify Darkseid's damage value by -2; damage from this attack is penetrating damage; 3) Darkseid's damage value is 0; if the attack succeeds, put the target in any unoccupied square within Darkseid's range to which he has a clear line of fire.

can he use his perplex to raise his range to a 7? or is it locked at a 6 range?

also/ DARKSEID'S MOTIVATIONAL TECHNIQUES :#(non-optional) When an adjacent friendly character makes an attack, modify that character?s damage value by +1 for that attack. If the attack roll misses all targets, deal the attacking character 1 unavoidable damage.

can this SP be used on Darkseid?

Yes, perplex can be used to increase his range (up to a maximum of 9 while using that option due to the rule of 3.) Nothing says the value is locked, so it isn't.
Sure. There's nothing that says it can't be.

thank you for the help