Impurities

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?

Walking with impure shoes on a carpet

Q: I stepped on some stool of an animal but was unaware until later in the day. The place I work is in a room that is carpeted. The day I was working, it was also raining making the soul of the shoe wet making me believe that the najasat has spread on the carpeted floor at my place of work. Now, as I work there on a regular basis I wanted to know:

1. If I would have to clean the carpet in the room?

2. How would I clean the carpet in the whole room as the carpet is stuck to the floor.

3. Would it suffice using a mop or wipes to just wipe over the carpet?

4. If I walked on the carpet again with wet shoes would the napaaki transfer from the carpet to my shoe to other areas e.g. car, home etc...

Doubts regarding impurity on the floor

Q: I had the urge to go to the restroom (for toilet). Before sitting on the toilet seat I usually check the toilet seat whether there is any thing on it or not (I bent my back while checking). The moment I stood straight, I was confused whether from the toilet or normal discharge that gushed out. It gushed so much (this time I really had the urge to go). It was watery and I am confused whether it was from the toilet or clear discharge and that I put my clothes on the floor. I am not sure whether the impurity touched  floor or not. Should I wash the floor? It happened to me nearly three times. 

Washing dishes with impurity on one's hand

Q: I had an impurity on my hand and it dried. I meant to wash it but I forgot and then I washed a pot (with my hand), heated up something in it and drank it. Is this pot (and what I drank) pure? I washed it under running water. Do I have to worry about the other dishes in the sink being impure since I washed the pot over these dishes (the water I was washing with ran all over them), or can I just assume they are pure?