Impurity on body, clothes or place of Salaah

Q: If you are wearing a perfume that has alcohol in it, can you pray salaah with that clothes?

Q: I have seen scores of pigeons roosting in many Masjids.  They keep flying around and a lot of their droppings are found on the prayer mat, some dry and some fresh.  I had the opportunity to witness so much droppings continuously being made by the pigeons roosting in Jama Masjid in Delhi during my visit once, when I had gone to offer my Dhuhr Salaah with the Jamaath.

I require the following clarification.

1. Is our Salaah valid if offered at such a place full of pigeons' droppings, dry or fresh?

2. Do we have to clean only the spot of the droppings if they fall on our clothes if we are in a state of Wudhu or do we have to do our Wudhu all over
again?

3. Similarly, I have witnessed the same scenes at many Eidgahs in different cities during my travel, during Eid Salaah, where sheep/goat droppings/cattle dung are found all around dry or fresh, which the people responsible for the maintenance of the Eidgahs neglect to clean. Is our Salaah valid in such places?  

4. What is the Shariah Ruling on these kind of najis?

Q: When praying at home where you are certain that there is no najaasat on the floor, will it be ok to pray directly on the floor? Or is it still better to use a prayer rug?

Q: I am working in a warehouse. There are two cats here. I took care of them when they were 2 days now they are at 6 months. They play with me and jump on me. I just wanted to know that I have only one uniform at the same time in that uniform can I offer prayer?

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.

Q: After wudhu can ladies wear lipstick and read namaaz or before wudhu?

Q: At the ground where one places his feets during qiyaam, there is less than a dirham najasah and one notices this after salaah? Is the prayer valid?

Q: If someone sees the imaam after he has led the salaah wearing slippers with pigskin leather inside-soles. Did the pigskin leather inside-soles make the socks he was wearing impure? The salaah he led was it valid or invalid for everyone?

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.

Q: Is it permissible for the female Muslim to be perfumed (be'd with alcohol or not) or to have lipstick while performing namaz and reciting quran?