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This is incorrect. A wing can impart momentum to air even in the absence of viscosity. However, the optimal wing shape is different. For an example of a wing that moves air "down" without viscosity, look at turbomolecular vacuum pumps:

http://www.physics.rutgers.edu/ugrad/387/388s06/UHV_LEED/UHV...

Not really - if a wing moves through fluid without viscosity it still has to move the particles down.

The impulse required to move particles of a fluid with zero viscosity would be zero, so the equal and opposite force that we call lift would also be zero. Consequently you couldn't fly if air had no viscosity.

If the particles have mass then the impulse wouldn't be zero.

Is there such a thing as non-viscous fluid?

Yes, one example is superfluid helium.

https://en.wikipedia.org/wiki/Superfluid_helium-4

Viscosity is weird.

https://en.wikipedia.org/wiki/Non-Newtonian_fluido