Does impurity transfer from trousers touched by a wet dog to my body and clothes if I am wearing them after performing ghusl while they are still wet, and what is the ruling on my prayer then, and how do I purify my body and clothes if the impurity has transferred?

You must ignore these whisperings (waswas) and pay no attention to them, for merely seeing an image does not build a case upon it. The default ruling for trousers that have been worn is purity, and the prayers performed while wearing them are valid. Abandoning prayers in response to these whisperings was a grave error, therefore, you must repent to Allah and make up for the missed prayers.