Is a zero-energy universe necessarily also a zero-information universe? The universe needs to be near zero energy to not crumple in on itself.
Under the same logic, does it also need to have near zero information content to prevent the passage of time from burning it to a crisp? (Landauer's principle applied over a nigh-infinite number of interactions)
If the negative energy is in gravity, where is the negative information that balances the system out?
Apparently negative information is a real thing - http://phys.org/news/2005-08-quantum-negative.html
 A: The universe needs to be near zero energy to not crumple in on itself.
Who told you that? A gravitational field is a place where the motion of light through space is curved and where objects fall down. Because space is inhomogeneous, this being modelled as curved spacetime. It isn't a place where space is falling towards the centre. The universe didn't collapse into some singularity when it was small and dense. Take a look at the FLRW metric and you can see mention of the homogeneity and isotropy of space. Because there's no overall gravitational field in the universe. Galaxies aren't falling towards one another, instead they're moving apart as space expands. 
Under the same logic, does it also need to have near zero information content to prevent the passage of time from burning it to a crisp?
No. Where are you getting this stuff from? Check out the heat death of the universe. But note the universe isn't burnt to a crisp. It just goes cold. The energy density evens out. So there's no available energy, so you can't do any work. 
If the negative energy is in gravity
It isn't. That's a popscience myth peddled by self-appointed celebrity "experts" who don't understand general relativity. See Einstein saying "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". Gravitational field energy is positive. When two objects fall together some of their mass-energy aka gravitational potential energy is converted into kinetic energy which is radiated away. So you get a mass deficit. But conservation of energy applies. You don't end up with less energy than you started with. 
Where is the negative information that balances the system out?
There isn't any. Information is just "pattern". Something you can make sense of. The alternative is chaos. Disorder. 
Apparently negative information is a real thing -  http://phys.org/news/2005-08-quantum-negative.html
Can you show me some? Can anybody? I think not. And as for quantum teleportation and quantum computation, do let me know when I can buy a quantum computer in Currys/PCworld. Quantum computing has been going now for forty years. And whilst ordinary computers have advanced by leaps and bounds and changed the world, quantum computing is still jam tomorrow, and tomorrow never comes. Do be a little skeptical about what you read in PhysOrg. And whilst Nature is a high impact journal, I'm afraid that these days you have to be a little skeptical about what you read there too. 
