Re: Is earth's orbit a helix ?

Quick answer; Absolutely, when viewed from outside the solar system
Long answer; your analogy with a bike wheel is spot on. From the position 
of an ant on the tire, the orbit of the tire around the centre is a circle 
(or in the case of us on the Earth, an ellipse). Once the ant looks at the 
surrounding scenry, it can see there is a motion associated with the 
centre of the wheel and so deduce that anyone looking back at the bike 
would see the ant moving in a cycloid.

Of course, not only is the sun orbiting the centre of the galaxy, but our 
galaxy is moving with the Local Group which is itself in motion, and so 
the overall motion of the Earth is much more complicated indeed.