I have some naive questions about polynomial-count affine varieties over $\mathbb{C}$:

1. Are all reductive algebraic groups strongly polynomial-count?

2. Are products of strongly polynomial-count varieties also strongly polynomial-count? What about (disjoint) unions?

3. If X is strongly polynomial-count variety, and F is a finite group acting on X, is X//F also polynomial-count? More generally, is the property of strongly polynomial-count invariant under étale equivalence.

4. If G is reductive algebraic group acting on a variety X, and the orbit-type stratification of X consists of strongly polynomial count quasi-projective subvarieties, then is X//G also strongly polynomial-count?

5. Are there general conditions on a variety X and algebraic group G for X//G to be strongly polynomial count?

Basically, I would like to know if there are operations that allows one to cook up polynomial count varieties from other polynomial count varieties.

See the Appendix here for the definition of polynomial count: here

EDIT: Just to be completely honest, when I posted this, I did have a sense for some of the questions, but I wanted to learn more about a concept I am just now learning to work with, and felt that they all fit a general theme so just included them all without detailing what I thought I knew and didn't.