Is it true that impurity does not transfer after the third contaminated object, and therefore the impurity of the flooring (the third contaminated object) does not transfer to shoes or other items? And is all the flooring in the house considered impure in the mentioned case?

It has not been mentioned in the words of the jurists that a third-degree impure object does not transmit impurity. Doubt about the transmission of impurity necessitates upholding the original state, which is purity (tahara). It appears that the questioner is afflicted with waswasa (obsessive whispering), so he should disregard it and adopt the easiest opinions.