My question is about non-probability sampling and the use of the aforementioned tests.

To my knowledge, both parametric and nonparametric have the same assumption that the data is from a random sample/random sampling procedures.

So how we handle the data from non-probability samples? Can we only complete descriptive statistics?

Also, I was informed there are such a thing as "non probability statistics", do these exist? I cannot find anything of the sort when I search.