Has that which was placed on the dry ground in the bathroom or the wet T-shirt that touched the bed or mattress become ritually impure (najis)?

The cure for obsessive thoughts is to disregard them and pay them no mind.

There was no need to repeat the Dhuhr and Asr prayers, because an impurity is attributed to the closest time it is likely to have occurred, and if there is doubt about the transfer of impurity, the default is that it has not transferred. All garments are presumed pure unless there is absolute certainty that they have been contaminated with impurity.