According to Wikipedia an airfoil of infinite length would create zero induced drag. Therefore, would it be possible to make a wing that creates no drag if you ignore viscous effects (skin friction) by walling it off on the wingtips to prevent vortex formation? Or is there another drag creating mechanism?
The infinite span has nothing at all to do with having no ends.
The ratio of lift to induced drag increases with span. If you fix the lift, and vary span, the induced drag will tend to zero as the span tends to infinity. That means in limit a wing of infinite span generating finite lift (and therefore flying at zero coefficient of lift!) will have zero induced drag.
This is a highly abstract approach to things and I don't think it provides any useful insight.
Anyway, forget about the vortices. They only happen behind the wing anyway and therefore are obviously irrelevant! Instead, call upon the good old laws of motion. The lift is upward force of the air on the wing. By principle of action and reaction (Newton's 3. law) the wing must apply force of equal magnitude and opposite direction, that is downward, on the air. Now if the ambient pressure above and below the wing is the same, this force will accelerate the air downward, which will increase its kinetic energy. And by law of conservation of energy, this energy has to come from somewhere and the only way work can be done here is by drag.
This suggests the way to reduce it. If the pressure can be increased below the wing without accelerating the air, there won't be induced drag. Well, that's exactly how ground effect reduces drag. Normally it does not eliminate it, because the air can still move outward, but a wing flying in a trench could perhaps get quite close (though not to zero, because the air still needs to move at least a bit to maintain the pressure difference).
You are describing tip plates, which you see on STOL aircraft from time to time, but which are actually too small to really do any good. I dimly remember that for tip plates to have any noticeable effect they have to extend at least a chord width beyond the airfoil. Because it's not just the air immediately adjacent to the tip that's curling around; it's a large package of air extending quite a distance, and to block it all takes a huge wall to get in the way. In which case they create so much drag on their own, and create all kinds of other issues, the benefit is mostly neutralized. Otherwise you'd see massive wing tip panels all over the place.
No, it is not possible to eliminate induced drag completely. Many parasite drag/induced drag graphs erroneously have induced drag approaching zero. And one certainly cannot ignore viscous effects or parasitic drag. There is no free ride here, although it is cheaper at Vy and at higher altitudes where thinner air favors greater ground speed.
But designers do try to approach an airfoil of infinite length by designing as high an aspect ratio as possible, as in sailplane. Also seen in nature with the albatross, this type of wing provides the highest lift to drag ratio, but at a cost. These wings will stall at a higher airspeed than a lower aspect ratio wing and have less stability in pitch. The stall angle of attack is also lower.
But the performance indicates why this type of wing is most efficient, and also why props are more efficient than fans. A wing creates lift in three ways, compression, mass deflection (action/reaction) from the bottom of the wing, and creation of lower pressure above the wing by deflection of air flow over the top of the wing. Of these 3, the third, created by the airfoil, is most efficient. Note, a long, thin, high AR wing will not do nearly as well with the first 2 due to pressure "leakage" from underneath, whereas a more parachute-like low AR will continue to generate more lift at a higher AOA before it stalls, just not as efficiently. The vortex lift from deltas, ditto.
There are also design considerations as far as strength for infinite wings, but for efficient cruising, we get as close as we can with high AR.