Well, i am FAR from a perfect barb--i mean, look at my main, I'm still in Hell!--but since i do not see any pro level 60's around, i will give it my best shot.
I am not sure what "optimal" DPS and health are for Nightmare, i am just running on what i have been using. I left nightmare a few days ago so its still pretty fresh.
Anyway, on your gear i see a lot of intelligence and dexterity, which are pretty much worthless for a barb. You socketed ruby to make up for the lack of strength. My strategy has always been to socket primarily with Amythists for the health bonus, and level up my rubies for weapons. I know that gear is impossible to find nowadays, but with Nerves of Steel you can get away with losing some armor value in favor of some STR and Vit. (case and point are my stupid act 4 normal gloves) More life=a barb that refuses to die=a barb that can hack on enemies for a long while.
As far as skills, i prefer to use Hammer of the Ancients over Whirlwind. Actually, i use Hammer with Thunderstrike over everything else on the board. With the Thunder-strike rune, every time you kill somebody, everyone else gets stunned. This is great because with the Hammer hitting like a freight train on its own, against trash you are guaranteed to be fighting monsters that are stunned 98% of the time. The stun also affects elties, so smashing a skeleton under a big scary elite will shut him up for a minute. With him shut up, you can make a run for the hills, or go ape crap on him and pop another stun on the snotty fallen that comes in to help him. Eventually, it ends up in WAY more stunlock than you can get with Ground stomp when in the Wilderness.
During Nightmare, i was using either Charge with relentless assault (the rune that makes it so the cool down resets when you hit 5 ppl) or ignore pain over ground stomp. Ground stomp was great during Normal, but i found in Nightmare that it had too much cool down and too little duration to keep the enemies down for long. The glory of using Charge is that you can drive into the mob of monsters, weaken them, turn around and charge back out, and repeat for brutal mauling. It also gives you a quick escape from some nasty spells like Arcane and desecrator. Having problems with a wasp or summoner? Charge right through his meat shield and kill him! Mobility makes it great. Ignore pain is good because....well...if you are ignoring pain, you are free to go crazy and put a lot of hurt on the monsters before you feel the hurt.
People LOVE earthquake, and it does a ton of damage, but with a cool down, i do not like it. Yeah sure, when you pop it it skips a fight, but there are too many situations when it does not accomplish much. People will say it is ultimate, it might be, but i am not a fan. I prefer War Cry for the armor buff, and in two levels when you hit 41, it gives you a sizable HP bonus as well!
As far as passives, i like ruthless and nerves of steel, but pound of flesh is iffy. Some people swear by it. I am not one of them. I like weapons master, because between it and Ruthless, your hammer of the ancients becomes GODLY, and since it is my main ability, thats what i focus on.
You badly need new weapons as well, are those the Bastard Swords you craft in Act 4 Normal? I am sorry, but my monk is using better and he is 6 levels under you. Once again, i know that finding gear is brutal, since all my barb rolls is Demon Hunter gear, but you need an upgrade. Try a 2-h weapon with a lot of vitality, (i started finding 2-handers in act 2 nightmare that gave somewhere around 50-100 vitality, which with nerves of steel made the lack of a shield hurt less) or craft the rare Ono from the Blacksmith. The Ono is the 1-handed axe, and it rolls some pretty good stats sometimes. IF you are still dying, maybe go for a shield. I am usually not one for charity, but i will look in my stash and see if i have one of my Barb's old weapons laying around, and find a way to get that to you.
Well, that's all i have to say. Maybe someone else can give you a professional opinion. Hope this helps!