Does touching semen, urine, and faeces with the hand while wearing gloves invalidate ablution (wudu')? And do clothes become impure (najis) if these substances touch them without knowledge or visible trace?

Semen is pure, and touching an impurity does not nullify ablution. Impure clothes must be purified for prayer, but there is no blame on you if you were unaware of their impurity. Dry does not make dry impure if they meet.