Does touching something Najis break one's Wudhu? If so, does it apply when wet or dry? What about touching something that is dirty but not Najis, is it then necessary to wash my hands?
Bismihi ta'ala
Touching something will not break one's wudhu`, unless it is the touching of a dead human body after it gets cold, and before it is washed.
For anything else, najis or not, just touching it will not break wudhu`. Of course, if it is wet, and your hand gets contaminated with najasah, all you need to do is wash it.
As for touching something dirty, the same thing, and no, from a shar'i perspective it is not necessary to 'wash' your hands if it is just dirty and not najis.
And Allah knows best.