Does the earth spiral around the sun's movement/motion path? I have watched the following video (How Earth Moves by Vsauce) regarding how earth moves:

                
            
Here are some screenshots:


I have some questions:

Does the earth spiral around the sun's path as it is shown in the video (exact time is 19:49) and screenshots? Is the spiraling movement caused by sun movement (on its path shown above) where the sun is dragging the earth (and other planets).
Does the earth go in front of the sun then back, then fourth and back like it is shown on the video? I see both the sun and earth racing with each overtaking the other over and over. Is this assumption true? In this manner, would earth, at one point in time, be closer to the destination where the solar system is heading (I think they call the destination Vega) than the sun?
I am working on a poetry piece. If I mention that earth and sun are locked in a never ending race with each taking the lead (earth moving in front of the sun's path / winning) and earth actually dropping out of the race (spiraling/moving out the race and falling behind), that they are destined to never meet (collide), would I be correct?

P.S. My knowledge of astronomy/physics is very limited. I have tried my best to be as clear as possible. Sorry for any confusion. Thanks.
Does the earth spiral around the sun's path as it is shown in the
video (exact time is 19:49) and screenshots?

The Earth does spiral around the Sun's path, but not quite as it's shown in the video.

It isn't clear if the video accounts for the 60 degree tilt of the Solar System with respect to the galactic plane.

The sizes and distances are not to scale.  The Sun and the Earth are depicted far too large with respect to their distance from one another.

The relative motion is not to scale. The distance from one side of the spiral to the other side should be about 2 AU, or 3x10^8km.  But the Sun is moving at about 200km/s around the galaxy, or 6.3x10^9km per year.  So the distance between two consecutive spirals should be more than 20 times the distance from one side of the spiral to the other!  This can be visualized as an overextended slinky.



Is the spiraling movement caused by sun movement (on its path shown
above) where the sun is dragging the earth (and other planets)?

No, the Sun's and the Earth's mutual gravity cause the Earth to rotate around the Sun.  The Milky Way's gravity causes our Solar System to revolve around the galactic center.  The Sun and the Earth are on the same plane and moving through the galaxy together.  The Earth would still rotate around the center of the Milky Way if the Sun magically disappeared.

Does the earth go in front of the sun then back, then fourth and back
like it is shown on the video? I see both the sun and earth racing
with each overtaking the other over and over. Is this assumption true?
In this manner, would earth, at one point in time, be closer to the
destination where the solar system is heading (I think they call the
destination Vega) than the sun?

If you consider a plane tangent to the Sun's velocity vector, then the Earth will pass across that plane twice per year, appearing &quot;in front of&quot; and then &quot;behind&quot; the Sun.  This is simply a geometric result since the Earth and Sun share another plane. I wouldn't call any future position of the Solar System a &quot;destination&quot; without evidence the Solar System was sentient, but I am not a philosopher.

I am working on a poetry piece. If I mention that earth and sun are
locked in a never ending race with each taking the lead (earth moving
in front of the sun's path / winning) and earth actually dropping out
of the race (spiraling/moving out the race and falling behind), that
they are destined to never meet (collide), would I be correct?

We haven't ruled out the possibility that the Sun may someday envelope the Earth: What will &quot;the Earth being consumed by the Sun&quot; look like?. Also, the Earth isn't likely to leave its orbit before that time, but the Solar System is chaotic on long time scales. However, your poem would be consistent with current models, and we (humans) don't conclusively know how the Solar System will end.  So my two cents is that your poem doesn't contradict modern astronomy.  Besides, what's the use of a poetic license if you don't use it?