Washing a soiled carpet

Q: I am having trouble learning how to purify a carpet. I honestly feel like I have transferred filth in so many places, it must be likely that my salah are not counting. What is the difference between a thick and thin carpet?

I put water three times on impure cat vomit while drying (not completely) with towels in between. But the carpet is thin enough that some water gets to the bottom if I saturate it with enough water. Did I do this incorrectly and now filth is transferred everywhere since later on peoples feet touched that wet area?

Paying for a service

Q: I work in a hospital in the UK and applied for a parking permit - I have to pay every month to park my car at the hospital. When my wage came, I realised the charges for parking were not being taken from my wages so I contacted them twice. They assured me that they had my account details and money would be taken.

A few months later I realised again no charges for parking were taken so I took no further action and left it because I thought I've contacted them twice and done what I could. But now I have a guilty feeling and think maybe I should have contacted them again until they took the money. Do I have to pay them back or pay the amount to charity? and am I at fault?