Does a fluid with zero viscosity cause a body moving through it to decrease it's velocity? If a massive body (suppose it's a square piece of metal, perpendicular to its velocity) is moving through a fluid with zero viscosity, does the metal feel a force decreasing its velocity?
I would say yes because the metal makes some part of the fluid change momentum, the effect of which is to change the momentum of the piece of metal.And because the fluid has zero viscosity (inner friction) the fluid can bounce back, without affecting other parts of the fluid, and won't create vortices.
 A: I believe this is a known paradox in hydrodynamics known as D'Alembert's paradox. The TL;DR on that is if you assume zero viscosity and a potential flow, you don't get any drag force, though this is counterintuitive.
The effect you're describing in the second paragraph reminds me of the phenomenon of induced or added mass - though that's relevant to accelerating bodies, and not to bodies with constant velocity moving through a steady-state fluid.
A: The perpendicular impact on the metal causes the fluid to bounce back and change momentum. Without any influence on the surrounding fluid due to friction forces in the fluid, which has, after all, zero viscosity. So no turbulence develops and the fluid on the side of the metal plate onto which the fluid bumps, is build up in two regions, which don't influence each other: a fluid layer with a velocity in the direction of the velocity of the metal plate (due to the change in momentum), and a layer which isn't affected by the plate (see picture). The fluid moving "outside" the plate flows around the edge of the plates towards the lower fluid pressure (created by the moving plate) without forming turbulence and the fluid behind the plate moves along with the same velocity, but lower density, and thus lesser momentum. This compensates for the change momentum of fluid in front of the plate, so no net force is created to slow the plate down. But it stays counter-intuitive. See picture below.(By the way, by now it must be clear that I don't agree anymore with me answering "yes" to the answer in my question).
If I make the plate bigger, the low pressure behind the plate gets higher, so more frictionless fluid is "sucked" in, with the result that the momentum change (due to a greater area of the plate) is compensated for by an adjusted decreased fluid density behind the plate. 
the momentum change due to the bouncing back of fluid from the plate is compensated by an equal, but opposite momentum change caused by a lower density of the fluid behind the plate. And thus is the net force (=dP/dt) on the plate zero. The difference with d'Alembert's Paradox is that in this case, the fluid is not incompressible.
So Of course, you can apply this reasoning to masses of any form.

EDIT1
I see now that although the fluid density behind the plate becomes lesser, the total momentum stays the same because of the greater area. The momentum of the two layers of fluid above and below the layer with a changed momentum due to the collision with the plate must of course stay the same, so there is indeed (as was my first impression), a net force that slows down the plate. I think that's because, in contrast to d'Alemberts Paradox, the fluid is not incompressible.
EDIT2
The density of the fluid behind the plate doesn't change, but the fluid velocity will be lower (like cars driving on a road with two lawns will decrease their velocity if they go over to a road with four lanes), so the total momentum to the right will be the same as the total momentum of the two layers with velocity to the right.
EDIT3

Last edit! See second picture. The fluid behind the plate is divided into three layers. The layer above and beneath have the same momentum as in the two layers on the left side, but the middle layer has a momentum that is less than the main momentum (this right middle layer doesn't interact with the two layers above and beneath it because of the lack of internal friction), due the low pressure behind the plate. The tube with the fluid is infinite long. So the plate is stopped to the point where it has the same velocity as the fluid, and the whole fluid is streaming to the right again with equal momentum everywhere. So as far as I can see, the motion of a fluid without viscosity will stop an object moving in it.   
One last last last remark. Of course, the fluid without viscosity can transfer energy to the plate. So it stays in motion. The question is how the fluid flows. This can be tested in an experiment with a superfluid in motion and placing a metal platelet in it, perpendicular to the direction of the velocity of the fluid. When you make the streamlines visible you can see if the second picture is a good representation of the real fluid. Of course, the momentum increase left to the plate is compensated by a decrease in momentum on the right side.
Over and out!
