Have you ever seen a pure blue sky without any clouds?

Yes where I live the summers are mostly clear skies which means hot and it is. If we do have clouds during the summer it will be August and September which is the monsoonal weather coming up Mexico way. Very humid with a chance of showers and electrical storms.

Well yes but not very often though.

Yes, during the time of year when fronts pass through. High pressure builds in, resulting in a blue sky for many days.

Yes. In fact the past couple of days, it's been a completely clear sky where I live. But today it's completely overcast again.

EDIT, Jamie, I think you are referring to blue field entoptic phenomenon (aka "blue-sky sprites). Apparently those are white blood cells traveling through the capillaries in front of your retina.

Yes I call it Idaho Blue sky - don't see it much on the east coast but when visiting Idaho it was a fairly regular occurrence.

Here on the downslope of the Blue Ridge Mountains, aka the Smoky Mountains, we have clear blue skies on occasions in the Winter and sometimes in the Spring and Fall.  In the Summer there is too much hydrocarbon haze from the tree emissions.  Here is a relatively clear autumn day that still shows the haze from the trees about 40 miles to the north on the way to Brevard, NC.

https://earthdata.nasa.gov/learn/sensing-our-plane...

Yes I have                              

In very hot summer duh! And you see the plane vapor streaks as well. 

Yes. Countless times.  

Yes I have.