The universe's resolution limit

Like the IceCube? Or do you mean low-energy neutrinos specifically?

https://icecube.wisc.edu/

The fundamental question is: if neutrinos provide a better signal because they overall interact much less than photons (a visible photon coming from the farthest corner of the universe will stop running as soon as it meets my eye; a neutrino can cross a star without noticing), how will you get them to interact with your telescope? That's a big problem for direction detection, too: with a telescope, it's easy to determine which direction the light comes from, as it can cross the front glass but not the surrounding casing. When a neutrino (out of several billions crossing your detector) finally gives a signal, you can't even know whether it's coming from the sky or out of the Earth!

To get better than a completely blurred image, you'd need some way to focus the neutrinos. That's where the fact that photons are affected by more things work in their favor for this use case.

Here is a link to the paper http://arxiv.org/pdf/1510.04996.pdf.

No, it's talking about optical resolution. If you were to make an image of the universe surrounding our Solar System and galaxy, there's a maximum number of pixels that you could zoom in and see before everything gets fuzzy due to spacetime warping the path of the photons as they made progress through the universe. (Like taking a photo through frosted glass, except the frosting is much finer here.)

Yes, indirectly: At the Planck scale (10-35m), a quantum foam of virtual particles appears and annihilates itself. While these particles are ephemeral, for a moment, they are there, with mass.

Mass affects spacetime, bending it slightly, changing the path of anything travelling through that spacetime. Think gravitational lensing, though on a much smaller scale.

Light travelling long enough, through enough foamy roil, will deflect a little, randomly. The cumulative effect would be to "blur" any images of sufficiently distant objects.

Or so the idea goes....