The sun at the north pole appears to circle you slowly, left to right, like a plane, for six months and then land (set) in September?

Yes... and no.

True. If you are standing at the pole, the Sun would appear to circle you (one turn in 24 hours). Until June 21, it would slowly climb in the sky until it reached an altitude of 23.49 degrees above the horizon. After that, it slowly creeps back down.

At equinox, it should in theory be bang on the horizon (centre of the sun's apparent disk), but the air causes refraction, so that the Sun would appear to be a little more than its own diameter above the horizon. You'd have to wait until, approximately, Sept. 25-26 for the top of the Sun to finally disappear below the horizon.

Still, it is not yet dark At our latitudes, we have between 20 minutes (in winter) to 40 minutes (in summer) before it becomes dark enough to be a problem. This period is called Civilian Twilight. People can continue their "civilian activities" (like driving a car) AS IF it were still daylight.

At the pole, you would be in Civilian Twilight until October 9 or 10.

After that, it is dark enough to see the brightest stars, but still light enough to see the horizon. This is the time navigators would take their sextant readings. It is called the Nautical Twilight. At the North pole, this would last until October 25-26. After that, there is not enough light to do anything outside... unless the Moon is out (for half the month, the Moon is above the horizon).

Finally, after Nautical Twilight, it is considered to be "night" for ordinary people... but not for astronomers. There is still some sunlight hitting the higher part of the atmosphere, giving just enough light to ruin "deep sky" photography of faint objects. This is called Astronomical Twilight. At the pole, this goes on until Nov. 13-14.

After that, you're in the dark... except when the Moon is there.

True. On September 21st is the equinox, and the sun would appear to set on the horizon, then dip below it - and, you're in dark for the next 6 months, until March 21st.

The sun appears to move clockwise in an up and down sine wave pattern low to the horizon, once every 24 hours, but never setting until September

pretty much. atmospheric refraction will make the sun appear to linger on the horizon for a few days.

because the sun is only just below the horizon it doesn't get dark immediately. the poles are astronomically dark (sun > 18 degrees below the horizon) for only about eight weeks.

Hmmm, ..., Were you asking if this was a true statement concerning the North Pole? If so the answer is Yes, that is a true statement.

You cannot turn a declarative sentence into a question simply replacing the period with a question mark.

You're right. I love this analogy.