It all depends on what you mean by " are ".   

Magnetic field lines have the same kind of reality as elevation contour lines on a topographic map of terrain. They are convenient mathematical fictions that allow us to describe consistently the direction and the strength of how "test particles" would move in the presence of magnetism. Just as a road really goes nowhere, but we travel along a road, field lines don't represent a "flow" of  magnetism, they simply represent strength and direction of how other things would "flow" in the field. The concept of the field is itself a metaphor, a very useful one.
On a topo map, when the contour lines are close together you know that there is a steep slope in the reality and a ball, for example, would roll in a particular direction (at right angles to the lines and in the direction of lower elevation) and speed (fast where they are close). If the contour lines are far apart, the real place is flat or nearly so and the ball will roll slowly if at all ... but still at right angles to the contour lines.
And just as a standard topo map has contour lines that are well defined (as to the elevation change represented by successive lines) so too does a magnetic field line have a specific definition in terms of mathematical relationships between the quantities of the field and the test particle.

Tesla's "rotating magnetic field" is of course composed of stationary fields from separate coils, energized in sequence around a circle. A "test particle" like the Egg of Columbus rotates because it is following the sequence of stationary fields made by the separate coils as they are energized in the rotational sequence. The fields themselves do not rotate. Tesla used 4 coils driven by 2-phase AC in his demonstration to produce the "rotating" total field, but the field no more rotates than would LEDs blinking rapidly in a circular sequence.

ETA: Tom Valone did a very interesting experiment that he talks about in the Homopolar Handbook. He actually mounted a simple LED voltmeter arrangement directly to the disk of a homopolar dynamo, connected at the center and the edge. He found that when the voltmeter rotated along with the disk, he could detect no voltage generated. But when the voltmeter was stationary in the laboratory reference frame, connected by the usual radial and axial brushes, he did detect voltage from the rotating dynamo.

Why would you get the idea that experiment conflicts with SR?  SR can account for a magnetic field as the result of moving charge due to the charge's FOR.  In order to induce voltage, we need a cross product of a time varying magnetic field across a conductor.  When the voltage detector is placed across a fixed radial section of the disk, the expected induction across that radial is very low as confirmed by the experiment.  But relative to the external contact it is another matter, which the experiment also confirms.

Why would you get the idea that experiment conflicts with SR?

I would find it very strange if your first rendering actually caused the magnet to rotate. This would mean an instant violation of many things. Can you show the experiment?

Ah...OK, I think I see it now. The magnet on the foil isn't rotating like a homopolar  motor, it's trying to slide, like a railgun armature, and the sliding friction makes it rotate. I think.

So if you had, say, a brass tube that would be a good fit for the OD of the magnet, or even better just a long skinny cylinder magnet polled endwise, and you set it onto a pair of rails and then supplied current to the rails, it would scoot down the rails and also roll. Maybe.

3)  The electrons are pushing against the conductive surface of the nickel coated magnet as they are being deflected by the magnetic field.  However, the force is perpendicular to both the velocity of the charge and the magnetic field, so this doesn't add up either. 

Dont remember if I posted it here also, with the mag on the foil, say a 3/8 lengh 1/2in dia mag, if I have the top contact wire in the middle, it rolls straight forward. Off center to the left, and it would go forward but also turn left. And likewise, contact to the right of center, forward and right turn.

Mags