Flashlight? Got headlamps? New moon 05-20-12. First quarter 05-28-12.
Ice axe? If you have to go up the chute, yes, definitely (hope you know how to self-arrest or glissade). The cables section is covered in snow making that section treacherous. Keep in mind that once the sun no longer hits the chute, it freezes making glissading "hazardous to one's safety."
Snow chains? No.
Altitude sickness? Sea-level devils are prone to AMS. Ask Dr. for Rx for diamox. If not, acclimate!
Harder? Whitney.
Two-ways? Up to you. Best advice: Start together, stay together. No "Saturday Night Specials."
Have fun.
