1. Well does 5e have anything similar to INA? I also feel like this feature could better be a soulmeld that goes toward survival
2. I believe this path of a barbarian almost could be like a sage or shaman type character who has more innate knowledge and mental fortitude rather than getting better rage. As such at level 3 he ought to be able to choose to be proficient in either Arcana, Nature, or Religion checks then either at level 6 or 10 he can be proficient in wisdom saves. I would also sprinkle in with Detect magic and Speak with Dead as rituals later on.
In addition seeing that bonuses are more rare I would suggest the essentia start out with one, maybe rage can expand it by one since it restricts somethings anyway. Finally in order to stop the of a long advancement chart for each meld or way too powerful to begin with in order to compete with more expensive items you could make a mechanic in which purposely unshapes a meld along with maybe 2 or 3 points of essentia burn to create a larger instantaneous or 1 round effect based on each meld. This at the very least come at level 10 if not 14.
3. Well I have played Incarnum before and is one of my favorites to use. Person Man, Grod the Giant, and Xefas I believe are the best people in sizing up and making homebrew melee characters. I honestly don't know people who play 5e so you may want to start a thread there and ask people to come over.