bathroom

Mopping a floor with an impure mop

Q:

1. My sister mopped the bathroom that my younger brother used, and the bathroom had pee drops on the floor as my younger brother doesn't exercise caution when it comes to pee drops. Then, not knowing this, I used the same mop and mop bucket with the same used water inside, to mop the whole living room. While the living room was wet, everyone walked all over it, and the wetness transferred everywhere in the house. By the time I learned a few days later that the mop had been used to mop the bathroom, all the wetness had been dried. What should be done in this case?

2. Also, my mother prayed on the living room floor (no prayer mat, just on the floor) many prayers. Does she have to repeat them?

Reciting duas and Quraan in a bathroom without a toilet

Q: A person has a bathroom with a sink, shower, etc. The toilet is enclosed in a shower door type enclosure. So the rest of the bathroom is not considered the toilet. Would it be correct to recite duas etc. there when making wudhu? Will it be fine to take a Quran inside the bathroom, recite Quran there whilst watching children in the bath? Not in the toilet, but in the rest of the bathroom.

Washing a tap close to the toilet

Q: I'm confused about the following:

In a combined washroom where there is basin as well as toilet. After istinja a person openes the tap to wash hands and then closes the tap. Is it necessary to wash the tap handle after washing the hands as the washroom is in common use at home and you dont know if some one touches with impure hands. What is the ruling for it?

Doubts

Q: I want to ask I was in bathroom but I utter don't remember muje bakshah dae ya al then I stop coz of thoughts. Actually in my heart was this muje Bakaah dae Ya Allah but I didn't utter full name Allah only I utter ya al I stop realize that I am in bathroom