Impurity on body, clothes or place of Salaah

Performing Salaah on the bare ground without a Musalla

Q: It is understood that performing Salaah/Sajdah in a place with najaasat is impermissible, with or without Prayer mat. But, I have witnessed many Muslims offering Salaah on the floor at offices, at railway stations, inside the aircraft, in trains, on the roads, on the deck of a ship/boat, etc. These places are frequented by many people returning from the toilets with their footwear on, which has a lot of najaasat. Will Salaah not be invalid for those who pray at these places with najaasat? I have had many debates with these people who justify that their Salaah is valid in these places.

Salaah with mazi on ones clothing

Q: Yesterday, when I went to toilet, I found stains of pre-cum (mazi) [I have this problem that often it comes out unintentionally). The stain was very small, probably smaller than a drop of water. Nevertheless, as I was in a hurry to join the Asr Salah in jamah, I forgot to change my underwear and even forgot to wash the stain. In this condition I prayer the Asr, Mugrib, Esha and todays Fajr Salah before recalling the incident. Now my question is should I repeat the four Salah prayed in the above mentioned condition or was my Salah valid. Can you also advise me on what to do for the problem of the mazi coming out.