I am really very humble. As for the rest of your comment, I need to get through the other classes to put everything into perspective. The fighter's superiority dice, for example, I may recommend changes to, and for the other classes. You say everything will be reduced to mediocrity, but I want to stop you there and say that it would be very balanced from what I am used to. The monsters wouldn't hit so hard, or have so many hit points. I want to use the original hit dice, such as 1-1 for goblins and 2 for gnolls. That is 1d8-1 (minimum 1) hit points for the standard goblin, and they just get a shortsword or spear typically, which does 1d6 points. You see where I am coming from? It's all different. I'm not going as far as to say 5th Edition should be a reprint of AD&D, it's just that there should be like a dial in the game to make it more like AD&D and BECMI also, in terms of power.
I'm the kind of player who never looks at the DMG or the MM, also. So all I know of the monsters is my expectations from earlier editions. I want to be able to join a 5th Edition game, say at a convention, and know how much it will take to defeat goblins. It's all very particular, I know, but I hope to find a proper balance between the old standard and the 5th Edition "modern" standard. I am not meaning to disrespect the 5th Edition or the modern standard.
Things sound very big to me, which your experience may show isn't. Advantage, for instance, sounds like a real big deal. Getting to roll a second die was unheard of, at least until the Choose Future spell from the Tome of Magic was released in 2nd Edition. I just don't feel the barbarian should be "twice" as strong as others with the same strength scores, or be able to fight with bonuses to damage without taking at least a small penalty. I am very much a believer in balancing things out that way, like the fumble with a natural 1 to balance the critical hit. Now I am maybe starting to rant, but I feel there is no other way to address your questions without explaining more of where I am coming from.
The barbarian's "resistance" to bludgeoning, piercing, and slashing damage is a 50% reduction by the book in 5th Edition. This, too, was just unheard of before. I don't feel there is anything about the barbarian that would provide that kind of bonus. That is the kind of thing I might expect from an iron golem in the new edition, or from skeletons vs. piercing and slashing weapons. The barbarian already has extra hit points that let him take more damage. Damage reduction 3, which is 3 fewer points per hit down to a minimum of 1, is something I could live with. If you play with much higher damage, this maybe should be more significant, maybe something like 5 or 4 + 1 per three barbarian levels.
The stealth only working for 1 minute is poor, I agree, but again I am of the mindset that the stealth actually grants invisibility and silence so it's supernatural and pretty cool for a barbarian to me. (Thieves' hiding in shadows and moving silently actually grant invisibility and silence in all of the campaigns I've played.) If the stealth is something less than this, of course it should be longer, but again it's like taking the rogue's ability to me, and the tracking ability of the ranger, too, if it goes too long and the party doesn't feel they need a rogue or ranger to do most of the stealth or tracking. The book has it unlimited if I read it correctly. I just think that is over-powered given these points.
Retaliation now, it's really something I need to re-examine after analyzing the fighter's abilities. Retaliation is something that was unheard of as such before, and I think if anyone can do it, it should be the fighter. I would hate to think the monsters can retaliate. That practically changes the tone of combat in D&D, if so. I mean, you take turns attacking, and if they can attack back on your turn that would be an awesome surprise or a shock. Everyone would want to do it then, and I don't see why other characters couldn't try it. I wouldn't have introduced such a maneuver with the barbarian. That implies it's something primal, whereas I think it should have to be more of a finesse maneuver. It's big, so I put it this way.
Of course, I am just throwing darts at a board. I hope to engender discussion from others who can make suggestions. Paraxis, the Jester, Zardnaar, and steeldragons are just a few of the people I know who are experts with the mechanics and at DMing.