Does touching a wet diaper from the inside, or touching its contents to confirm a daughter's urination, then touching other things such as a mobile phone and household furnishings, cause these things to become impure?

It is forbidden to touch impurities without need. However, there is no harm in touching them out of necessity. If a wife comes into direct contact with impurities, she must purify whatever this impurity has touched. Furthermore, the default state of things is purity, and one should not deviate from this principle except with certainty, in order to avoid obsessive doubts.