Assalaamu alaykum. For all this time (more than 10 years), all the people in my home habitually walk in and out of the living room and toilet with their slippers on. In other words, we have been using slippers to walk around all around the house, be it the latrines, the living room, or the kitchen. There is one exception though, which it is the prayer room. So I think some impurities might have been transmitted all around the house, and particularly the living room, by way of the slippers. So I do not know where exactly, and I am not sure where the impurities are, because the water and impurities under the slipper cannot be distinguished from one another. Based on what I have said above:
1) Do I have to purify all around the house?
2) As I take off my slippers before entering the prayer room and there is wet liquid under the slipper and I step on the wet liquid and am not sure if there are any impurities, do I have to purify whatever space I have stepped on, and also the prayer rug, in order to perform my prayer?
3) Let us say that there are impurities on the living room and that these have dried up without leaving any trace, smell, taste, or color, and I step on it with my wet foot, will the impurities be transmitted to my foot and thus to every space which I have walked on?
I am from Malaysia, so apologies for my bad English. I hope that my questions can be answered in order to clear the doubt in my mind. Regards.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

You should ignore all doubts and suspicions and not give them any consideration at all. Verily, getting carried away with them leads to grave evils. The basic principle is that the bottom of the slippers is ritually pure unless you know with firm certainty that it is stained with impurity to the extent that you can swear that this is true.

Hence, you are not required to purify anything; and none of these places are ruled as impure, let alone considering that the impurity was transferred to your feet or to anything else merely based on these doubts and suspicions.

If you know with certainty that a specific area is impure, then in this case you are required to purify this area only. If you have walked over this impure area with your wet feet, you should simply wash your feet. However, all this is to be done only if you are absolutely certain that this area is impure and that you walked on it after it had become impure. If it is only a matter of doubts and suspicions, as is clear in your question, then do not give any attention to it.

Allah knows best.